{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook, we will use a multi-layer perceptron to develop time series forecasting models.\n",
    "The dataset used for the examples of this notebook is on air pollution measured by concentration of\n",
    "particulate matter (PM) of diameter less than or equal to 2.5 micrometers. There are other variables\n",
    "such as air pressure, air temparature, dewpoint and so on.\n",
    "Two time series models are developed - one on air pressure and the other on pm2.5.\n",
    "The dataset has been downloaded from UCI Machine Learning Repository.\n",
    "https://archive.ics.uci.edu/ml/datasets/Beijing+PM2.5+Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import os\n",
    "import sys\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import seaborn as sns\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#set current working directory\n",
    "os.chdir('D:/Practical Time Series')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Read the dataset into a pandas.DataFrame\n",
    "df = pd.read_csv('datasets/PRSA_data_2010.1.1-2014.12.31.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the dataframe: (43824, 13)\n"
     ]
    }
   ],
   "source": [
    "print('Shape of the dataframe:', df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1021.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>1.79</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>4.92</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-11.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>6.71</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-21</td>\n",
       "      <td>-14.0</td>\n",
       "      <td>1019.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>9.84</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-20</td>\n",
       "      <td>-12.0</td>\n",
       "      <td>1018.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>12.97</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd    Iws  Is  Ir\n",
       "0   1  2010      1    1     0    NaN   -21 -11.0  1021.0   NW   1.79   0   0\n",
       "1   2  2010      1    1     1    NaN   -21 -12.0  1020.0   NW   4.92   0   0\n",
       "2   3  2010      1    1     2    NaN   -21 -11.0  1019.0   NW   6.71   0   0\n",
       "3   4  2010      1    1     3    NaN   -21 -14.0  1019.0   NW   9.84   0   0\n",
       "4   5  2010      1    1     4    NaN   -20 -12.0  1018.0   NW  12.97   0   0"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's see the first five rows of the DataFrame\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Rows having NaN values in column pm2.5 are dropped.\n",
    "\"\"\"\n",
    "df.dropna(subset=['pm2.5'], axis=0, inplace=True)\n",
    "df.reset_index(drop=True, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make sure that the rows are in the right order of date and time of observations,\n",
    "a new column datetime is created from the date and time related columns of the DataFrame.\n",
    "The new column consists of Python's datetime.datetime objects. The DataFrame is sorted in ascending order\n",
    "over this column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df['datetime'] = df[['year', 'month', 'day', 'hour']].apply(lambda row: datetime.datetime(year=row['year'], month=row['month'], day=row['day'],\n",
    "                                                                                          hour=row['hour']), axis=1)\n",
    "df.sort_values('datetime', ascending=True, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1baff987b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let us draw a box plot to visualize the central tendency and dispersion of PRES\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.boxplot(df['pm2.5'])\n",
    "g.set_title('Box plot of pm2.5')\n",
    "plt.savefig('plots/ch5/B07887_05_06.png', format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v49YvA6Cqb6W0JtcPAEdEzgGOwx0NZ1TU5yXATqAm8nfP91NSXl5LZdToKOXl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bb03e30da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df['pm2.5'])\n",
    "g.set_title('Time series of pm2.5')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('pm2.5 readings')\n",
    "plt.savefig('plots/ch5/B07887_05_10.png', format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TXtD8DRuNH8ZvXvll+H2LnKUxnxalV9hmV3ny88cLclwv8uGmWLRmYR4kic7U\nr563/bY+k2K5X2JlODjemyjrpxOU38QcDL33o4mBxxpePwIIk0+9sEo9nKUebqC0UA1QZ55cRGFZ\n1rrUdXkUldhd8fhObnr/X7bf1ne2WK6OyiLdiyi0drbyv08fKrYYrqxsW8H5U8/m0+VzC3L8slbq\nI29b13e90zL386nfeci9QLD1VHD3Sw7Jpj5YPJMVrcuzlud7csvajrW88+3beT2mH/Obv2bIzf15\nbN7/gjcOoKfkLrfKUTyl3vPVxtXvjqO5SC6zIG5+/wYe1P/l5KePty2f+P5Ejn7ssC4XP+n5T6eX\nUIF3hXeroi+4+yXiCzG/+WsOfHhvDnh476x1UXoVetkngducNeU0Dn/0wEjydYWguP0oQ+bOActi\nYXWvFcv90hss9Q+aem6Ka7MU5NIWew/y9MdP542Fr/Ph0tldOn7ZKfUuRb/4qAHzuG5K3arIC63U\no1qUC1cbvuKvXWLGo8jqFk/tZMpXz4Y+Xj6I59HNY72vP1Qn5+24UenoAZZ6b/CpF+vedMQ7mPrV\nFN/8QOb985Kxq41mz386eSbKQGmUBsDvuFblWOiXLepAqZc8UUIaAaorChuVkYtVujaV5iAfWBut\n7lIYbve/WKGVVvyUTpjn9KD+L79/9f8K2tMoVlriG2dez0lPH8+Vb/3ZcxtTV3jJ2NXxm7JT6oXG\n7UXtTks9TAGHpC2CwjvdQRS5awqs1HOhtbPVd30UldJZBLfH058/mbWswzpQWiz3S0XXlM75U8/m\nrjl3sLwtXArjz1Z8yq9ePC+dRC4MxZpt+86itwB4e+EbntuklbqXpd7F+yszSn2IatXHiAW6Xwr9\nIUa21L2yTSbtSn1t51r6+cyG7Q1d8q5g9al3l6W+YPX89N8NNf0B++SyYrkYKiy2YCKZoCLHZ7+m\nYw2D69YJ3O5nz53Gh0tnU1dVx9/2ujbUsQuh1Fs7W5mzZBajh47x7MWbRpWbYm5a28RPJp+Ufm5e\nMlbFuqaWS/tLdKFLH4KPO6YiVkksFgu01AvxIVqP71WRyXNfjwiXJEnbuqBqPz2pCg8YoX9mVkEv\nolh+xbDUreGLg+sGA9BhG7voPqV++Rt/SP9tKqzfvnIhw24ZyNqO3NxcYfczBw7vnDM+9LEL4ab6\n1Uvncdj/DuCZL57y3MacR+DmQrl91s2899076Zz0Xt9tRUXX1HL5KXXHB7nIMu26K1TGKkNZ6oWw\nIKwvRNRg1I2+AAAgAElEQVRGw0+eRCKzLij9QKEmKoERZ/6jZ06ItM9zX07OqwzF8KlbC5Akk0n0\nsk+46NXf2JZ1F854eYC7P5wAkHNitqWpakmFIJ+D5CZPfPYoAO8vnuG5jVlq0G3cwVn1zNrwrOlY\nnQ8RjfPk7Ui9BOcH6XczowyUVlVUhbPUC/Ahdlrye4d5ma33wLPWqsP9Yo2O6VvVN2v7MI1Vrhkq\nH5/3qOe69xa9w0lPHZdldee759DS2WI9el6P7cX3Bm1hOWOSQx/Zn6aWxbZlPYFce6K3zbq5EOIA\nhQlpDPP+mhPr3JR6ZVi3Shd1RNkpdSdR7p/fQ62MVYSz1AtQrcY6ONoZsYBDwmNg1el++dMbl6b/\n3rD/xgyqHcSWg7fOHCfEdTl9r7sMHxtKRj9Fcczj32fq189nxaRX+Qzc5tK4LLdMzuouC7ktnhno\nTSQTrO5o7pbzBuG8/iiK3GpEHLLRYXmTyUmxGjzzW6xw8an7DYBaDciuyl52Sj3KCxnl469IuV/c\nrLjCu18yirwzok/dawaqM/rFmgI2nuyk0lHxKMx15Tqg5ocZD+z0oVb5fEC5fDStFku9uxSGtXfg\ndn+LFf3ivP4o96M17h+R1Nsxn1OFi+4IGwoa9Rt2UnZK/ZvV39h+R/kwfC31ipADpYVwv1heAmf+\n7SA8B1aT3iGNHYmOrDJ2Ya7LqdTzcS+8Yn79LPVcmGOZ5dddutQ6kOg6U7mHuF+i3BBr7yPsYOZu\nI/YAYFj98Ghy5ZnMu+Z9vQmf6Bc//WHtbVuLjOdCt4Y0KqWqgTuBjYBa4ErgI2Aihok7BzhPa51Q\nSp0JnA10Aldqrb2HnCMwxTGAli93SGXaUs+mO90vf3vnSv5vp99F2NfdXfPQ3Ek8/fkT6d8Jhx++\nKlZl6zLm4n7JRSmFzUef79qpz37xdPpvN7mvfncc7y16h0lHePv/o5BMJvnlSz9P/3Za6oarrzg4\nlVqU3qd17kBHiFnIAPXV9QAM6Ts01PYLmr8J3qhAzFliNP5uusAv7NcaaPDGwmldkqG7LfVTgKVa\n6z2BQ4AbgeuAy1LLYsBRSqlhwAXA7sDBwDilVG0+BHDebL9W1zlQ6jdwanatguPUC+t+CYP1mr2s\npWvf+zufLPs4/Xufkful/+5MdGZZImGuK5aH183ZhfVKz1DIySdmOTkrV787jpfmT83beVe1r7T9\nTiaTDKodlP7dt7q+xxQ5P9Alb5AXrTlY6lHHQG6fdUuk7fOJeU1Tv34+a52f+9H63lT1shmlDwFm\nwGsMwwofDbySWjYZOADYGZimtW7TWq8E5gHb5UOAfFiL7sf1dr9Yz5HvD7Ej3sGTnz2W8/5B6YdN\nNhqwcfrvzmRnliWci089l3uRpdTTXWL7dl4DwNZ9omCN+Hlj4eue2w27ZSATZt8W+fhOWh1utCQJ\ntlpnG5s8q9pX8ta3b3b5XFHpyjdjtdQLlSQt3720O2bdysNzJ6XDWm+YeV3gPgdueHDWMj+lPmH2\nrem/E13USd3qftFarwZQSjUADwOXAddorc2raAYGAP0Bq6liLg+ksbHBd319vd3gv/CVnzPjbPe4\n04HLMx9yY2MDdbXeftqhjQOIxWJUVlVkyfDNqsyl9K2vCZQxCn97/W9cNu1i27Kg4/fv3ye9TZ/6\nzCvgt199v4zc8WQntdU1VFkmSQwY2CfwvJWOSRXV1ZWe+1iXN/Srs+xTZVsXi8UgCX36VtuW1y+v\nAeAfB/yD372QcUc1NjZQ16fa9jsM2wzdhncWvBNqv4tf+y0X7fcbz/VhWLMik8GvvrqeJEka+tan\nl5mhjUc+ejDJ7ZJ5faeC6Nev1vN8AwbY3wPndn3bM41ybZ/sb8WNmlrjHa2sjIXavqG+j+13RUX2\nflHu1yWvZ7szvfYf0TCChc0L2XDw+lnb9O/XJ2t7c5vrpl+dXjari+GY3Z4mQCm1PvAocLPW+n6l\n1D8sqxuAFcCq1N/O5YE0NfmHfW07YEfb75mLZnrus3JlZqCqqamZ9nZv62/5srWQjNHRGc86XqIm\nY8WuWr02UMYwtMXbaOtsZdoXb2WtCzr+qlUtNDU109jYwLKVmW399luxag1NTc10xDtY1rIMNWhL\nVlhiw5cua6apxv+8FY6OYXtHp+s5GxsbbMtXNVsiT+Ix2zrT6l6zps22fNkKY/5Ba4vdNdXU1ExL\nS7vtdxja2+1WZdB+XX3G363IhFAOrB3E2o41EPfulufjnQpL8+pW32/GXOd8jgDfLsk0Vsubm0PJ\n3ZH67jo7E6G2b2u1f6eJRJKmpmaSySRLW5ey8YjhTHjrHr6/yZHUV9ejl33Cv2Zcy7g9r2ZA7cDA\n44P3/U4kDPu0tbUja5s1a7KDGArx3LrV/aKUGgpMAX6vtb4ztXimUmqf1N+HAq8B7wB7KqXqlFID\ngC0xBlG7TOgJAC74x6mHjX7J+fQ2drxnazabsD5zl9vzmI8dsXvgvtbuc9hUveY1rGhbQZJkVs6O\nMDNKs7uf0W+G8xheyZHMSSBdzaNhErVLvKptZfBGPpgzeLcYvCX9awaQIElNRU2XjpkvuuJCtLpf\nrnvvH74pap3MXvJBqHN7uV+ueutytrprE/a/Z3/On3o2f5x2CQAnP308D8+dxM3v3xBaliDcXFS5\nTr6LSnf71C8BBgF/UEq9rJR6GcMFc7lS6k2gBnhYa70IuAFDwb8IXKq1zkuAa5SBrCgPoaqiulvT\nBJjd77nLtW15W2drpEIZQdP/TUwftRkyWVtZa7s/YaJfupLL3sRZdcdroNQcPHabBJILUXPqbD5h\ngy6dzxxw22O9vaiIVZBMJqmtzLgO8+037i6ccerr39YYqaybmTfFD6948PGzjQHUN+YbGRQ/aJoJ\nwLJWI1tka2f4BubzlZ+5LvfTGW4+9UIMdne3T/2XwC9dVmUNn2utxwPhM/gAZz5xJn8d6z+IkYwQ\nUpgV/eLzwEKnCShwINqMxdO5+t1xXLLrH0NtH9VSNweLaitr7bPgQjRWzo8mlxfa01J3HMsM83Sz\n1HN5BlEb464+Z/O5VFVUp+vFWiOOqiuqu73Wq0lXrq3NJR3yw3Mf4OJdwr2vzqggN7zykTt76eY7\nY767USbH7XrfDiz+ebRyeW4hjfGkER689TrbdrnikUlJTT66Y+YdgdtEtbjCUsyEXk6un3FN6G3D\nhpXFTaWeipaprrS7AoKu68nPHs/LNHfnB+tlqfvl4MjlGSRJeFqAhXimZmRITUWNYamTtDVcxSqE\nDV10v7jMKI2StvnfM673tJJNvJ6Tc5ax+dzSU/sLnD7a7fjme7rj0J3yd568HamXEMU3ml142mdb\nn5WFjFPffOD3spaFHeyB8DNQ05Z62v1iV+pBVqPbLLlcLD5nfLyXpW7KW1lRyeKfr2JU4w5pl0Uu\nGSXjibjt3F1JdxyGtKVeWUUFMZLJRPqcx27+g7xm9etO3AqX7DxsF999rN/htIWvccCDe/lu75Ui\nwiuc2fTruynd1RHvc9R32szV1NVZpFZKTqn/Yuo5vuujfIBRraEw7pd8W3VBPYP0dtZqR5Z9wvoR\nTZ+6+QHUVNpDQ/0ahzcWvM7L81/0lSks2VaYh6We+lhMRV5jaYRyOW+ChM2PbVPqIapNRcXsQVWn\n3C9rO9em88P/YdfL836+KHQpTj3ekrUsqhspqMcXdiwsmUzw3drv0r+d4zUAs5s+iCSbH27fZVCd\nglwoOaU+Sd/vuz6KUq1xWKNBL4upXvzOme/k/YvWLPI9n98yyOTiCLq2hMP94rw3bT6TmI5+vKvZ\n+Kxuh3ADpW7ul7QPNUefuvVY1vs5b8WnkY8XRKdFqXtdc7Homk89u/HPJYHVx0s/8lxXVek+nyRr\nNjlJW4/Hy+cdBf/vKPu+dSY7827olZxSB5i7THuu85tp6MSZFCroYwrjUw87g9Pk1W9eZnmrdy1H\nN6vFzcXj9eKY3WGnknZivtzmQKkzvK49Yf9Y2+JtTP1qim8kTljVYKsK4zGj1Bkraj5n07q2P5sc\nlbqlW2/92Fe0Lc/avn9NqLlynphRScY7aH/vCu37dRJU69VKUC+oxdVSDzB0XL67vSft6rm5W75/\ncMkumUzaGmrrfW3tbCWZTObVtda3qj5r2e7378R5L5yVt3NAiSr1WUu8Z2RFaRWzfXMBSj2E+2XK\nV+Er8sz8bjrHP3EkRz12aOh9IFpGP3PgqjogBtrpU69xhDQ6G6sr3/ozJz19PDfOvD684B7MXjIr\n/bezeoz5ITqfq2mpm42A9dnkYhklkt7ul3X7NGZtf8CGB9l+J5NJJsy+nc9CWvUZ90uVi6XefZ/t\n3GWaDW4fYlvWlYHSO2Zlp1CIWgMgiC9Xfh5qu0QyYYuOMu9zW7yNDW4fwolPHZtXK7rapQextHUp\nj3z6YN7OASWq1H1LtDlCGv0mdDhnQAYRxlK3JskK4stVX0TeB9zHDbzuSXqSTkA89+Pz/se3qxem\n08H2rbZbQ05rbtqC1wCYsfg9z2OG7cZbXWphE3qZ0TpWS90kV6Vud79YCpO4+ISdvaV3Fr3Nxa/9\nhj0f8B8UNDHj7CsrqrIH7LtpEgu4J6bqCmZIorVUX5BPPcr1tnS22Kbc+x0nSdLW+zKf78rUxLGX\n5k+1RdpYi8JA+Bqr6fN1UwK2klTqfsnonQovSihRoE89hKXuJoMX+Yxp98rpblqEfvcMjElO577w\nM9Z2ppS6o4vrHCg1z+F3z/ITp546lqdPPbN9V+6n0/1ij37JVkrOCBvTRRN2ULDDx6deaPdLMpnk\nppk3MLvpA/70xiVuW3T5HJtZorbyGW8fpZj4vBWf2nzz5n21fgsXv5bJ4TO03p769z8fTYwkW3eE\nM0MRcr90B3VV2YlzTLIUbF4jF4ItdTC6d30r3P1+VvLZsrvN+Fy0ehEtKSXtrGTkxhsLX+f7mxwB\nQH11P5t13+bIjW3eh+5yFTgbj7Slm+ped7VcWDwZp66i1vbb7W+TrubNNxWdu1IvrKU+Z+lsLn/z\nMs/1+XgvrbNj86nUo45Z/fCpY9J/B72rzute1uY91uW6fzdlwC9JS91roASyFazfwKnzITgHSo/a\n9Fj7+hBFMsC7OMADn9zHrvftwOr2Ztfzh8V1QNf5QrYuZfi1w9OhhkGWuonZ5ayv7uvwqWcs9XFv\nX8FHS41UPb6Weh5e8oRHjyDuMlAKZBXU9sKpHOKJTqotA+dWS9wteqOrVllHekZpFc3t9sHwqO6X\neCIeSXGuaM0e+M03VvdLUERYlOsNO0PaDfMb8Hp29uLj8PWqr3I+lxs7r7dzXo5TkkrdLxVA9oBa\nbpb62aPO46JdLs1aHs5Sd1fqF7x4Lp+v/IyXXGK6u4pThgWrF9h+h80lsqZjDQB9q/vZjmkNVfvn\n9MyM1nyH33nVmHWexxx8Mz/UKD71Bc3fMPK2dfmDJaXx6o7V9K/t73oMt+pR5vovVn7OXXOCZzo7\nsbpfZi+xx0pHdb/s8cAYNrtj/cgyeJFrY2x9dtb3LWqRFydLW5am483D5jJyw+wBefWy3llkz4j6\nRYgB2Q+XzGHSJ8aYUFAPJ0rOJj9K0v3i99E6u8p+7he/l7dPZZ+sBiGsTz1oVmmYWohRceafyXXw\nzYzrra+uTw9GguFSam5fxai7t7Rt76eA8nF9Xr77RMKcUerI9+GYbu/G24uMwhO3fXATf9l9HPFE\nnLZ4G/U1mZA0s4e3umO1a3SSuX7/B/dkdUcz5476RZTLSlucbllFo1rqn62YF2n7rvQy/L4Za2+h\nX00ms7ZX8fOwbHmXUcBl9mmfdmkeiBkYEXbW9/Tv3uXzFfPYZOBmntvs++BuAOy+3p6BjWGUjJV+\nlKSl7jWjcsZ379mqwkM0K8H6MdVW1bJ+g5GJ77Stf5peH8ZSD/vR5NMHF3SssDKtTEUvNFTbCwC0\nJ9p459u3suLmo7hffv3yL7lj1q0eW7vvk/7taalXpFZnGkrnMZrbV3HUY4e6znrtTHSmwz6tET/m\n/Zr53XRXOc2uuXk/vlgVLswuc15D0bmFwfXxcS/68fDcSSHP7a8Y/RrFWU0fpHtzTsyJbjsOGW1z\nkS5rWeq6PcCny+fyzBdP+spjctlrv++a+yU1RuQWyFBf3c91n6+bvw517OunXxv4ja1pd79vUSlJ\npR53uXkPz53EIY/sx2XTLnJsG95KsHbxayvr6Fvdl0XnruAfe/8zvT5U9EvAOXNxWQztO8x3fVC+\nk7BK/UH9XwAG1w3mX/vdnM4z0x5v71IO6dUdq7n3o7tcq8z4Yd5vZ/hpJlQzO6TRGb3x0NxJvLlw\nGic8eXTW8ad/915aGVn9wOYz9GosP15mn/FoLVz9s+d+4nk9GfkzcerrWHLXH7rx4a6KPgz3fXRP\nqO2CLGc/A+Fv71zJKU+f4LrOHBsY0W+kzf3S7lOA+tcvX+Ari5VlrUu7WCLP2/0yoGaA67iTWRTb\nSTKZZN7yzJyENxe+HmhYbT9se/YauS+3HBDdXWelJJW6m4IylZETX/eLQxFaFYP5MK3uhbxb6o7z\nf75iHn95809Zg3iX7Xo500/1ryGS5QLysnhDUlNZyzbrbsuLJxj1Or1mHfq1T9bra+nInmloMrhu\nMBv038hVTnP8xNkQmu4PN/dLFPdCkmT62vpUZ5S6eYxcXEhPfPZo4DYdltS7P9769PTyOw++N/L5\nTMJO8unqLMppC19zXW4W7F7S0mSbre3n7vAKKnAjnoz7WuqBM8JNn7pbT5+kq65wRtpZdcTXzV/a\ntgt6VyorKnn4yMc57nvujWJYysanPtBSid1KruFUx23+g6xlhlIPlidIqXhV8zn28SNYuGYBIxvs\ng14DawcGTvMPCrGL6kc1z2cm9mqPt3fJR+738SaSCSo8LH4vn3pW7hfLB/vpcvusTv9Y+kTG/WJx\nGQRZ6l2l05bQK2M4OLNU+vHVqi9tLqWw73qg+yXHa25JNY5jhu3CQstAvZ9hFSWQIZFM+PrUg95P\n06XoJo+njB4D92BPetenqk/gfZu+0N2VF5USVerh44b9lJlfSGNfl26XUQTZZYq+My9JjjHMC9cY\nH4IzF0yQQk8J4SkPRFfqZg+lNjUjty3hPsjj/1Fm5PAbJEpazhc2+iU9ozRmd7/cNuvmSMUIFq/9\nLj0QarXU851C2UmHw32UC4c+sh9LWpakf4cdPwoabMy17TYzNNZV1dmmxvsr9fBGl5+l/vmKeSxt\n9fbdQ+Zdcs+d5C6j9bv598zr+XbNQsB4H62pN95Z9FZW9IyTr1bmJ0SybNwvXkor166m28cW2v2S\nCLDULYN6JlZF7py9WV0R7GMNUtpeVsSDRzzmu1/GUndXyn4pea3ntLqUnB+yc4p+ev9kMt0YeE4+\nqkgNlKaWP/VZ9vX4WepPfvZ4+u/aylp+vNUZKZlMBdA1Sz2ZTHLGs6dy/8d2t0ra/dKFGqtWhW4c\nMz9KPVfMIAWnyyLu8T0kk0nXcFEvEsm45zXuev+Orsud5/OSx+u41gbpL29mqjcZ5QeLU1O2bJS6\nlzUQJZlQrjk38hH9MvrebdN/O3NbhLHUg8Iq3ayTnYbuzCYDNvU9rukOSCQTrg3DlK+eDZQN7INl\nq9uNsMl4Is7DcyfR3L4qY6lbzrHYkgvba/KRMyQwauFxawNTW1WbjmXOuF/cn2VYC/vbNQt56vPH\n+dVL59mWm42SVxpZK2Hfp7AKMtBSz9H9Mm2BMf7ibKDd7uGf37iMEbcOTudhCUOQ+yUI87rcetJe\nPQave++sDBaG7YZuF3kfN0pSqU9b8JrNAu9MdHp2l31nlDre3aCXOWz0S5D7xVRQ1hlsfoUBnBkW\nnQruy5VfcNXb9sIKzh5KkiTfOXKzV8QqAie6mFEnuVQTst4rq0VvyvbIpw/y8xfOTMmSbak/bQl1\ny5p8lLbUK23r3a7Hv2pV5j7VVNbYGjHnNdj3C6dove6vdfJRWk4PoyJsb3NQ3eBQ20Wdah+WWz74\nNwBTvpzMn8ZemV7uJv/N799APBlPuzPCMHPxDK55d1yX5XQ1Cj0tdffnXFtZEzkFSb7S/JakUv/P\nx3dzbyrZzuqO1Yy4dTDPfeme8jaKzy6oqx3W/RL08DoS7dw15w5bMiE/qgOswhOePNoWo+w2kp9I\nJtj2bntpvIpYRWD6gIyvO8H85vlZ673ie63ZMRc0f8MnSzOZKM379Y3leG4+9X9Nvzb9d/ZAqV0p\nmuvdBmSzJi5Znpf1/aiprEk3YkEfbFi3jNd2mdwvwRa/1zu8wxC7y+HITbNDNt1wKvVjNz/e9rvL\nLieS7Dw8k60ynowze8ksfvzMiSwL8HsH4QwljSSX6X5xebZePQAvY7Gmsta3Yd9xyOisZflK+FWS\nSh3gve/eAYKn8nq1tJBtmQdVVSJPlvr4Wbfy+1f/z/9cFoK6emYKXyvO63aztGOxWLClnlo/c/EM\n10bIq5Zmn+q+6fu7w71bceHL56fXmcutYW/mxB9Tyub2VTYrzmlsm7HW5jFMa9zNN+q01K2TZ6zu\nueqKaipSlrr5MXv13pIkWeozqea0yT/KOj4YDdxbC9+whTQG4aVwsnpwIdMLOBu+jfpvbPvtds11\nlXWhjm3KNdjSa0gkE5z81PE8++Uz3DTzBs/9btw/Oxe7FwdscFDwRg7M65rxXXa6aK9G3NzHrRi2\nl245c9tzeODw/4U+R1RKSqnfc3RmckVYa8LPam5zqXwOcOFodws6hn/uF6tV68fCgC7n7iP2tP0O\nM1DqJMun7iJ309rFrm6PX+746/TfsViMGLHAupFOqiuqAl0XtmgjxyxKpyJzHuqTVErVKof8Ybq4\n1ggKa0igzVJPHcfPunr68yc815mzJJ3XscO9W3HkY4fw1rdvpOSvCgw3mfypey/U6dcPk3vkxpn/\n4suVdiOgIlbJ7J/MZfxBEz33HT10jO+xrQyvH06tpRGIJ+N8t9Zw/fn5xA/b5Aibsp6zxDuKadvG\njH/ajI8PIplM8q/p1/LbV34VantIjSUlk+x63w625TfOvN7zOz9oo0MZWJcdYv2nvf8U+rx+lJRS\nt1qVZpHeoA/Cb/DoyjczN/msKael/zYjIJwEuV/MSAanIli8djHnTz07/XtAQCk05zlyUepu7hcn\n3zTPd7XUP10+1/Y7SoKpGDFO3OJHpCu6+vRsbGkZUlE25rU7kx9Z5V/SsoRPVxgymgON5rHcnrfT\n/dLYZ0jWNmBM2U/71EOEpYYZUOyMu79/X636Egg3UHriIye6Tv7Kdp35yzNJ388Vb/6B/3x8t215\nRayCofXD0g2r23WFSd2898h9ASMZ3oh+67HFYCNPkHXcwu9dqqDCFqd/Xmq8xY0VEfKqmyRJZo09\nhdnHqwfvZXm7DaJv0LAhJ297cqRze1GySj0MVRVVaX+kmwX3ftPM9N+Pzct0l7ymNQcNlJoP0/mw\nr3rrz7YZr0EDWm8sfN32Ox9K3c2qWLdPo2uFdWcujij3/fp9b+KG/W4xzukxS8/tHpoupvcWvc2B\nD+2d5VYzleyM797jG0s+DqdP3ep/9hovqKtydyVUV1RbBoZN94s3QT7SRz99mD0e8Ldwqyuq0i6Y\nIX2Hem433yUHyWsLXokkz+sLXnVdXuHIn+NGUOUsgBH91gOM2dgVsQoeOfIpwO6m8HuXDHdg5jyt\nHj1pyC0UNNeKWK9+87LrumMfP9x1udOldvRmx/LGyfmZeAQlptTdZtv5WUt1lX2IJ+N8vPQjht86\niAmzbw91Hq+JMl6W+m3TDV+gWTXI+fI4y2J9nbLSwlIRYZYh4FpQ16uuaRiFHUWp/0CdCLgrWZOE\ni7+6JvUhtHS28EHTTK52RDkkkgk+WfYxhzyyHwc9vE96ufPjdha3ePrzJ7Msda+UB32q+6Sv1VRE\nXRk0PPt5e4/v3UVvZ21TXVHNz7Y9m/03OJDbD7rL81huja+TYFnd12eFILocJ0w+fvO5mtua9/JJ\ny9wBvxKSzoF7v/GwMGMRTvzmVHiRy/N3NoADaweFm0AYkpJS6lblMjCVaMqPmlTX1qxMHjbaZOMB\nm7gu97Jkpn4x1fbbOSjp7I65DWz6kUs+amcop1dmS7cGwzkIFVapV1VU2a41SdJ1BqApyz0f3mnZ\n1/6Rmj5n6z5ug+LOkEbn4OXpz/4oy+LzsgBrK2upqLCPi/jWw41o+f334/9kLauqqGZg3SD+e/gj\njB2xu+e+YQZBg9xBW6/rHidtHjvT+EV3v9z8/r/TbopM2bhsma2zdp1UYFfqCZ/xkSjpFExafCx/\nLxLJROT5K2bv0ZqoLZ+UrFJf0baCeCLu25K6DQIGsduIPWyluJy4ne+3u/0WgNGpeqhOhdrVmpO5\nZKZzuj3cBqiSJF0tp3O3t+cGD3sfrS+/6aryOi9kuuuQPcHKuV9LZwu3vP/vwHO7NchO15OXpV5X\nVRc6pNHtuLkQNqrkzjnjs5YNcuQ7ClLqG6WSpjlZnBrEtBotzrBHP3dHW7yNP7+RKShjKmY3xevn\neozFYukZwuA/cfDwTY70XOeFNS13UNZTE7+CPF70rTJSjGSKpueXklLqzi7gY/Me8X2Rw5Zws+3j\nY5F4uV/MlK3miH9QxsSojBqyfeR9skMa3TPTuX14e6y3V+TzOcm4X7KV46LVhhKxzmYN6k7f/eGE\nLOvddr7UB2Rm19x23VHpdZMcGTy9op7qquqyJh+d9qz34FbU5+qaujhkGubbPrgpa5nzngV5CsyZ\nvE5un3WL4zjJrBJ7fj71prWLbb/N3p+bMdDhM/HJmAyX2acz0eFptG3j0evwY7IlPfJ3axdx0han\nBO6TTCZdwxn9MCNf7jjoHjYduBnn7/DLaIIGUFJK3fkBvN8009dSzyVZkjNEznb+VFAjwGvfvJLO\n52F+rG41EJPJJKs9YrnDsNU622T1HMIogjChfclk0rXhy0qelWOmSy/3y9gJYwH7farJwUfqhmnh\nWwC/3CgAABrBSURBVC3/DywD4h8umcOlr//edV+bpR7y/hWLZDJJU4uhTH+1o+FWDGpkgsNSM899\nVbt9+r5f+gVrWUBjW7tP3YpbjyNz9pjtfWzzyOFvbhvEYRsfYfs9Z8mswH2cGCGN0az1utT3utt6\ne/DmyTPY0KOHlCslpdSd1ua+6+/nb6nnotT9LHVL9MtxTxyRzueRLuQQs0dOAOz34B62AgpRcVpB\nofZpafK0Rq2EHSh1RgNt6lPey8RsGPy60Nb7lMvAl+18qY/cdBt4DUyZ5cfcsFrqYbrdufh188VK\nS0jfTsOMCJsgH7/T+vYiSZLm9lW2ZX7X2s8xq9jMn+NmMHyx8vOsLKQmsZhdqZ+85ak5RaxMPGoi\n9xz6QF4SbiVJMnbEHpH2qY0wUSsXSkqpO2OXqyqqfX2ftRXRH2pU94u1fJpbSGOUNLBumNZYFK54\n8w+c+8LPQm0bRqk7P6ywL62XT91cZ7PUc/gA/7rHPzI/0jNK20OlP3CjrqouPWhoTjpxw0yBUKhs\nh0G8+s3L/GvGdUAqH7tHfn4nQUrdWjt3lUOp+70nmw9Stt9pn7rHM/DLPWNtPAbWDnRV6hMOvse3\nt3rcVsdxyMaH2fKdO1lwdrh0BQlHecS/7B6ce6Yr6ZTDUFJKfcpnU2y/44m4Z9iTGrQF+21wgO/x\nBrsM2vgNCLnFqceTmcFa8yU2u2v5KDTbP2CiUlfI1X1Q5/OxmJgNoJcb45znz7B9sF6x+AdueLDn\nORr7Zk8i+mzFPGoqanLKuGkfKE14WomZdMSGUv/L7uPsDYwHTpmu3zfbT+5k3/X3BzKzjJPJJMc/\ncSQ3vf8vAI7c9BjXVM5uBLkBrYrSmiHTTfZbP7gx/XdLpz1k12wAvBoCP+vb6lM3vm/7+zNm2C4c\nsenRAYVPjPswvH6E5zbVldWux7jzYHuEkrOQ+UEbZRchd5JLucoolJRSP2FrexmoJAnPgZf7vv9Q\noEW58/CxWcv8BoTcLPXORGd6mTlAZOYlyWXWm5NzRp0XvFGO5DqAW+sxecf6sWYSbLlbs4/Oe8Tm\n4vBS6io1K9FVDsvztZ6vNd4aOg+KFcP9krHUvXqBZqisGfc8ot9IfrbdOYHHd97vzQd9z2PLDHuO\n3AfIWH9rOu3Fi2sra31DEa04XSp+cgalxP3jtEvSf7c4ir2bjZ6XcnOWnrx+35v45mwjN7z1+0sk\n41lFq49NVSTzU5xmY3LBjhdy9qjzuHL3v/lei5UdhuzI7J9kZlQnkol09snfjrnYM9y5OykppV5b\nZbcQ44m4rWyWFSONqv3ynS13Z8rS2s3iM/PPx51dzq4z2Zluyc3jnfrMD4HcJjs4KWxXLlsJhIkq\nqHG4tbxm0ibxL51mjYzxmi7vN1nF6rJxWl252EpWS/3l+VM9p4dbS/xB9qzWsISZKVyTcq+0xlvp\niHcwu+kD2/r7P7k3tKXulXzNxOrGcTYAbtf2cdPHDLm5Pze/n0nSddZ25/qGBANZU/XrqurSz9Ka\npCyRTLLDvVvZ5QhhBdfXGBFQ/Woa+Mvu4yIp4j7VfRhaP4yr9vg7YB/T+r5LGOVOQ3cOfex8UVJK\nfezIsWnLBSBBMstyMamprMkK8bJOw04mk7zwteHOsb6EQQOlThY2L2DxGuPBO/2Q/57xT89jhcXN\nxx8r0GPddt1R/OewSYHbOafZm7UfraQHSn0iZ6wFmr1S0Pp9xNbn5twuly6wdaD0rjl32CrdP3fc\nS+m/zUbNHEA2LXc3d54fYQaHYzGjd/j2t2+y3m3rpEvvpWWurEu/D2ZPYMqXk5m7TGcdy8unvn7D\nBulzeW3rNlC64+3Z1YbCuCecWHtcWw7OKHG3npLZuERpQJ2+dS+3zA/VyQxOTRgyrf3fvXph5jgu\nY3T9atxTTxeSklLq1ZXVPHLkExyz2XGAYal7uV/61wzgno/utC2zugKsL0xYpV5fXc/q9mabotrj\ngTHc+f6drvtO/HBC0CUF4qbs1no0ZFFxWna/3/kS24QgL5xurYZaD79/MmlLhXvPoQ94HtM64Gel\nIqRSd4ZE5uJTr62q5atV7nUkt2vMzBUwrUqzJ2Yq52NdipX74aYkonLF7uPSyjiRTNDa2copz/zQ\nNeeMl0/9kl3+aPttDJTa3S8NNf2z9vOaxBUV6xjND7c4mZ9vbzSmbj3dtFKP0Gg7G6Rxe17jeoyz\nRv3cdiYn1S69yX4uBk2hKSmlbrLTMKPLE0/GaXNR6qOH7kRVRRXLHKFT1nhr6wi8VUn5uV/W6bMu\n8WSc5a3LXdfnWg7PD7eB212He4flRcFZqDfszFenpd7f5YPPDJQa9/zXO/2eQzY+zPOYXlar37iI\nVak3OAaUzUHrDRo29NzfSXVFNR8uneO6zqoYnAO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qYVFKVQA3A6OANuBnWut5RZBjBkYJ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\nU4+I6JA09YiIDklTj4jokH8B1GvI2gZt70AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bb045a3b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HvJPOeGfNyDmbz1QU54rN9qeaoRPCbI1CsUC+mLc851bNc/aTSvdp4HJgdyHE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bb02f59668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's plot the series for six months to check if any pattern apparently exists.\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df['pm2.5'].loc[df['datetime']<=datetime.datetime(year=2010,month=6,day=30)], color='g')\n",
    "g.set_title('pm2.5 during 2010')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('pm2.5 readings')\n",
    "plt.savefig('plots/ch5/B07887_05_07.png', format='png', dpi=300)\n",
    "\n",
    "#Let's zoom in on one month.\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df['pm2.5'].loc[df['datetime']<=datetime.datetime(year=2010,month=1,day=31)], color='g')\n",
    "g.set_title('pm2.5 during Jan 2010')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('pm2.5 readings')\n",
    "plt.savefig('plots/ch5/B07887_05_08.png', format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient descent algorithms perform better (for example converge faster) if the variables are wihtin range [-1, 1]. Many sources relax the boundary to even [-3, 3]. The pm2.5 variable is mixmax scaled to bound the tranformed variable within [0,1]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import MinMaxScaler\n",
    "scaler = MinMaxScaler(feature_range=(0, 1))\n",
    "df['scaled_pm2.5'] = scaler.fit_transform(np.array(df['pm2.5']).reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Before training the model, the dataset is split in two parts - train set and validation set.\n",
    "The neural network is trained on the train set. This means computation of the loss function, back propagation\n",
    "and weights updated by a gradient descent algorithm is done on the train set. The validation set is\n",
    "used to evaluate the model and to determine the number of epochs in model training. Increasing the number of \n",
    "epochs will further decrease the loss function on the train set but might not neccesarily have the same effect\n",
    "for the validation set due to overfitting on the train set.Hence, the number of epochs is controlled by keeping\n",
    "a tap on the loss function computed for the validation set. We use Keras with Tensorflow backend to define and train\n",
    "the model. All the steps involved in model training and validation is done by calling appropriate functions\n",
    "of the Keras API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of train: (33096, 15)\n",
      "Shape of test: (8661, 15)\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "Let's start by splitting the dataset into train and validation. The dataset's time period if from\n",
    "Jan 1st, 2010 to Dec 31st, 2014. The first fours years - 2010 to 2013 is used as train and\n",
    "2014 is kept for validation.\n",
    "\"\"\"\n",
    "split_date = datetime.datetime(year=2014, month=1, day=1, hour=0)\n",
    "df_train = df.loc[df['datetime']<split_date]\n",
    "df_val = df.loc[df['datetime']>=split_date]\n",
    "print('Shape of train:', df_train.shape)\n",
    "print('Shape of test:', df_val.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "      <th>datetime</th>\n",
       "      <th>scaled_pm2.5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>25</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>129.0</td>\n",
       "      <td>-16</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>1.79</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 00:00:00</td>\n",
       "      <td>0.129779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>26</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>148.0</td>\n",
       "      <td>-15</td>\n",
       "      <td>-4.0</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>2.68</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 01:00:00</td>\n",
       "      <td>0.148893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>27</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>159.0</td>\n",
       "      <td>-11</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>1021.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>3.57</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 02:00:00</td>\n",
       "      <td>0.159960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>28</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>181.0</td>\n",
       "      <td>-7</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>1022.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>5.36</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 03:00:00</td>\n",
       "      <td>0.182093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>29</td>\n",
       "      <td>2010</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>138.0</td>\n",
       "      <td>-7</td>\n",
       "      <td>-5.0</td>\n",
       "      <td>1022.0</td>\n",
       "      <td>SE</td>\n",
       "      <td>6.25</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2010-01-02 04:00:00</td>\n",
       "      <td>0.138833</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd   Iws  Is  Ir  \\\n",
       "0  25  2010      1    2     0  129.0   -16  -4.0  1020.0   SE  1.79   0   0   \n",
       "1  26  2010      1    2     1  148.0   -15  -4.0  1020.0   SE  2.68   0   0   \n",
       "2  27  2010      1    2     2  159.0   -11  -5.0  1021.0   SE  3.57   0   0   \n",
       "3  28  2010      1    2     3  181.0    -7  -5.0  1022.0   SE  5.36   1   0   \n",
       "4  29  2010      1    2     4  138.0    -7  -5.0  1022.0   SE  6.25   2   0   \n",
       "\n",
       "             datetime  scaled_pm2.5  \n",
       "0 2010-01-02 00:00:00      0.129779  \n",
       "1 2010-01-02 01:00:00      0.148893  \n",
       "2 2010-01-02 02:00:00      0.159960  \n",
       "3 2010-01-02 03:00:00      0.182093  \n",
       "4 2010-01-02 04:00:00      0.138833  "
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#First five rows of train\n",
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>No</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>day</th>\n",
       "      <th>hour</th>\n",
       "      <th>pm2.5</th>\n",
       "      <th>DEWP</th>\n",
       "      <th>TEMP</th>\n",
       "      <th>PRES</th>\n",
       "      <th>cbwd</th>\n",
       "      <th>Iws</th>\n",
       "      <th>Is</th>\n",
       "      <th>Ir</th>\n",
       "      <th>datetime</th>\n",
       "      <th>scaled_pm2.5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>33096</th>\n",
       "      <td>35065</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1014.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>143.48</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 00:00:00</td>\n",
       "      <td>0.024145</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33097</th>\n",
       "      <td>35066</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>53.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>7.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>147.50</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 01:00:00</td>\n",
       "      <td>0.053320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33098</th>\n",
       "      <td>35067</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>65.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>151.52</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 02:00:00</td>\n",
       "      <td>0.065392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33099</th>\n",
       "      <td>35068</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>70.0</td>\n",
       "      <td>-20</td>\n",
       "      <td>6.0</td>\n",
       "      <td>1013.0</td>\n",
       "      <td>NW</td>\n",
       "      <td>153.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 03:00:00</td>\n",
       "      <td>0.070423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33100</th>\n",
       "      <td>35069</td>\n",
       "      <td>2014</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>79.0</td>\n",
       "      <td>-18</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1012.0</td>\n",
       "      <td>cv</td>\n",
       "      <td>0.89</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2014-01-01 04:00:00</td>\n",
       "      <td>0.079477</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          No  year  month  day  hour  pm2.5  DEWP  TEMP    PRES cbwd     Iws  \\\n",
       "33096  35065  2014      1    1     0   24.0   -20   7.0  1014.0   NW  143.48   \n",
       "33097  35066  2014      1    1     1   53.0   -20   7.0  1013.0   NW  147.50   \n",
       "33098  35067  2014      1    1     2   65.0   -20   6.0  1013.0   NW  151.52   \n",
       "33099  35068  2014      1    1     3   70.0   -20   6.0  1013.0   NW  153.31   \n",
       "33100  35069  2014      1    1     4   79.0   -18   3.0  1012.0   cv    0.89   \n",
       "\n",
       "       Is  Ir            datetime  scaled_pm2.5  \n",
       "33096   0   0 2014-01-01 00:00:00      0.024145  \n",
       "33097   0   0 2014-01-01 01:00:00      0.053320  \n",
       "33098   0   0 2014-01-01 02:00:00      0.065392  \n",
       "33099   0   0 2014-01-01 03:00:00      0.070423  \n",
       "33100   0   0 2014-01-01 04:00:00      0.079477  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#First five rows of validation\n",
    "df_val.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Reset the indices of the validation set\n",
    "df_val.reset_index(drop=True, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1bb049fd940>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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ciMwAanBDFi8BT4RqlWEYRj8kqyCr6hnAgcBOqtoFnKyqZ4VumWEYRj+jKtsBInJ7wt8A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\nPhPqle39AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bb045e7c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hN4osymQwGDKFUcgGg8GQEYxCbhQT4+FlDAbDSo1RyGnjyNJx5RVNFsRgMGQdo5ANBoMh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\nlKs2vmpS7+rI4LdDSnlr+R/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QIyWodxNyg7TdeL2y84pB6+T5DZqExkamM6W5HgrPPauW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\niEIWBEHIE0QhC4Ig5AmikAVBEPKE/wA3EMAi1fn6gQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bb0499dc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The train and validation time series of scaled pm2.5 is also plotted.\n",
    "\"\"\"\n",
    "\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df_train['scaled_pm2.5'], color='b')\n",
    "g.set_title('Time series of scaled pm2.5 in train set')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('Scaled pm2.5 readings')\n",
    "\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "g = sns.tsplot(df_val['scaled_pm2.5'], color='r')\n",
    "g.set_title('Time series of scaled pm2.5 in validation set')\n",
    "g.set_xlabel('Index')\n",
    "g.set_ylabel('Scaled pm2.5 readings')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to generate regressors (X) and target variable (y) for train and validation. 2-D array of regressor and 1-D array of target is created from the original 1-D array of columm log_PRES in the DataFrames. For the time series forecasting model, Past seven days of observations are used to predict for the next day. This is equivalent to a AR(7) model. We define a function which takes the original time series and the number of timesteps in regressors as input to generate the arrays of X and y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def makeXy(ts, nb_timesteps):\n",
    "    \"\"\"\n",
    "    Input: \n",
    "           ts: original time series\n",
    "           nb_timesteps: number of time steps in the regressors\n",
    "    Output: \n",
    "           X: 2-D array of regressors\n",
    "           y: 1-D array of target \n",
    "    \"\"\"\n",
    "    X = []\n",
    "    y = []\n",
    "    for i in range(nb_timesteps, ts.shape[0]):\n",
    "        X.append(list(ts.loc[i-nb_timesteps:i-1]))\n",
    "        y.append(ts.loc[i])\n",
    "    X, y = np.array(X), np.array(y)\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of train arrays: (33089, 7) (33089,)\n"
     ]
    }
   ],
   "source": [
    "X_train, y_train = makeXy(df_train['scaled_pm2.5'], 7)\n",
    "print('Shape of train arrays:', X_train.shape, y_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of validation arrays: (8654, 7) (8654,)\n"
     ]
    }
   ],
   "source": [
    "X_val, y_val = makeXy(df_val['scaled_pm2.5'], 7)\n",
    "print('Shape of validation arrays:', X_val.shape, y_val.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we define the MLP using the Keras Functional API. In this approach a layer can be declared as the input of the following layer at the time of defining the next layer. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.layers import Dense, Input, Dropout\n",
    "from keras.optimizers import SGD\n",
    "from keras.models import Model\n",
    "from keras.models import load_model\n",
    "from keras.callbacks import ModelCheckpoint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Define input layer which has shape (None, 7) and of type float32. None indicates the number of instances\n",
    "input_layer = Input(shape=(7,), dtype='float32')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Dense layers are defined with linear activation\n",
    "dense1 = Dense(32, activation='tanh')(input_layer)\n",
    "dense2 = Dense(16, activation='tanh')(dense1)\n",
    "dense3 = Dense(16, activation='tanh')(dense2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multiple hidden layers and large number of neurons in each hidden layer gives neural networks the ability to model complex non-linearity of the underlying relations between regressors and target. However, deep neural networks can also overfit train data and give poor results on validation or test set. Dropout has been effectively used to regularize deep neural networks. In this example, a Dropout layer is added before the output layer. Dropout randomly sets p fraction of input neurons to zero before passing to the next layer. Randomly dropping inputs essentially acts as a bootstrap aggregating or bagging type of model ensembling. Random forest uses bagging by building trees on random subsets of input features. We use p=0.2 to dropout 20% of randomly selected input features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "dropout_layer = Dropout(0.2)(dense3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Finally the output layer gives prediction for the next day's air pressure.\n",
    "output_layer = Dense(1, activation='linear')(dropout_layer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input, dense and output layers will now be packed inside a Model, which is wrapper class for training and making\n",
    "predictions. The box plot of pm2.5 shows the presence of outliers. Hence, mean absolute error (MAE) is used as absolute deviations suffer less fluctuations compared to squared deviations.\n",
    "\n",
    "The network's weights are optimized by the Adam algorithm. Adam stands for adaptive moment estimation\n",
    "and has been a popular choice for training deep neural networks. Unlike, stochastic gradient descent, adam uses\n",
    "different learning rates for each weight and separately updates the same as the training progresses. The learning rate of a weight is updated based on exponentially weighted moving averages of the weight's gradients and the squared gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_2 (InputLayer)         (None, 7)                 0         \n",
      "_________________________________________________________________\n",
      "dense_5 (Dense)              (None, 32)                256       \n",
      "_________________________________________________________________\n",
      "dense_6 (Dense)              (None, 16)                528       \n",
      "_________________________________________________________________\n",
      "dense_7 (Dense)              (None, 16)                272       \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 16)                0         \n",
      "_________________________________________________________________\n",
      "dense_8 (Dense)              (None, 1)                 17        \n",
      "=================================================================\n",
      "Total params: 1,073\n",
      "Trainable params: 1,073\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "ts_model = Model(inputs=input_layer, outputs=output_layer)\n",
    "ts_model.compile(loss='mean_absolute_error', optimizer='adam')\n",
    "ts_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is trained by calling the fit function on the model object and passing the X_train and y_train. The training \n",
    "is done for a predefined number of epochs. Additionally, batch_size defines the number of samples of train set to be\n",
    "used for a instance of back propagation.The validation dataset is also passed to evaluate the model after every epoch\n",
    "completes. A ModelCheckpoint object tracks the loss function on the validation set and saves the model for the epoch,\n",
    "at which the loss function has been minimum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 33089 samples, validate on 8654 samples\n",
      "Epoch 1/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0190 - val_loss: 0.0199\n",
      "Epoch 2/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0165 - val_loss: 0.0117\n",
      "Epoch 3/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0163 - val_loss: 0.0123\n",
      "Epoch 4/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0162 - val_loss: 0.0162\n",
      "Epoch 5/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0161 - val_loss: 0.0124\n",
      "Epoch 6/20\n",
      "33089/33089 [==============================] - 4s - loss: 0.0161 - val_loss: 0.0132\n",
      "Epoch 7/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0160 - val_loss: 0.0140\n",
      "Epoch 8/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0161 - val_loss: 0.0133\n",
      "Epoch 9/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0161 - val_loss: 0.0120\n",
      "Epoch 10/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0160 - val_loss: 0.0122\n",
      "Epoch 11/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0160 - val_loss: 0.0123\n",
      "Epoch 12/20\n",
      "33089/33089 [==============================] - 3s - loss: 0.0160 - val_loss: 0.0119\n",
      "Epoch 13/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0160 - val_loss: 0.0123\n",
      "Epoch 14/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0159 - val_loss: 0.0132\n",
      "Epoch 15/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0159 - val_loss: 0.0118\n",
      "Epoch 16/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0159 - val_loss: 0.0120\n",
      "Epoch 17/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0159 - val_loss: 0.0124\n",
      "Epoch 18/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0160 - val_loss: 0.0120\n",
      "Epoch 19/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0159 - val_loss: 0.0122\n",
      "Epoch 20/20\n",
      "33089/33089 [==============================] - 2s - loss: 0.0160 - val_loss: 0.0137\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1bb05ac8fd0>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "save_weights_at = os.path.join('keras_models', 'PRSA_data_PM2.5_MLP_weights.{epoch:02d}-{val_loss:.4f}.hdf5')\n",
    "save_best = ModelCheckpoint(save_weights_at, monitor='val_loss', verbose=0,\n",
    "                            save_best_only=True, save_weights_only=False, mode='min',\n",
    "                            period=1)\n",
    "ts_model.fit(x=X_train, y=y_train, batch_size=16, epochs=20,\n",
    "             verbose=1, callbacks=[save_best], validation_data=(X_val, y_val),\n",
    "             shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction are made for the pm2.5 from the best saved model. The model's predictions, which are on the scaled pm2.5, are inverse transformed to get predictions of original pm2.5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "best_model = load_model(os.path.join('keras_models', 'PRSA_data_PM2.5_MLP_weights.01-0.0117.hdf5'))\n",
    "preds = best_model.predict(X_val)\n",
    "pred_pm25 = scaler.inverse_transform(preds)\n",
    "pred_pm25 = np.squeeze(pred_pm25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_absolute_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MAE for the validation set: 11.6757\n"
     ]
    }
   ],
   "source": [
    "mae = mean_absolute_error(df_val['pm2.5'].loc[7:], pred_pm25)\n",
    "print('MAE for the validation set:', round(mae, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S09PJyMgEYMSIUQ3237VrFwMHDiIhwfLkbrjhlw3e37p1C/v27WXmzBtwu52Ul5dTXFzM\nzp07GTbMKkk6cuRoJc6KTsW1djUA3lHBwcBt2zSqqjRGjrTsCl/fvjjXr0MrK8XMygbghBMscd6z\np2vNFoxLcW4Lqakwf351hxX31v2eSf/+A+jevTtXXfVz6upqee21l8nJyaGyspLS0lKysrLYuHE9\n3bv3sPc94YQ+7Ny5nfr6etxuN/feeyczZ97ur2xn0K9ffwYMOJEnn3yG7t3Tee65vzBo0BAGDhzI\nunVrmDjxdDZu/C6yF6hQtII9GDjqZLst4DePHOkDwNe3HwCO4p14/eLcq5cl3Lt2qci5y5CaSofX\njL344u/z+98/zM03X0dVVSWXXnoZLpeLW2+9k9tuu5m0tAycjUpxZWVl8eMfX83NN1+Hpmnk508i\nN7c7I0aM4uGH7+fpp59j3LhTufHGazAMH0OGDCM3N5ebb76Vhx++n3/+8+9kZmbidreDb6NQHCPh\nxHnNGktwR42yvodGH0uc9eJi8OdCp6ZCRobJ7t1dK3JWVeniDHWN8UHcXaNpkiP6Y2RlU7rEEunc\n3DSmTPGyYIGToqIKMjLAPfc/ZFxzFZUPzabm+pvs3SdPTqakRGfLlthKdFZV6RQKRVSj79iOXlbW\nIL/ZNK0c5/79DTIyrDajT19r++KdDfbv3dsqxN+VpnErcVYoFBHHzm8OGQwsKYHDh3Xbbwbw9bUG\nzh3FxQ32793bsj127+46khURz1kI4QJeBgYACcDDQDEwDyjyb/aClPJtIcS1wPWAF3hYSjkvEn1S\nKBSdhyvMzMAVK6zHgN8MYObkYCYloZc0FmfLydy1S0M0Py8rrojUgOBPgENSyp8KIbKBVcCDwFNS\nyicDGwkhegK3AOOARGChEOJTKeXRzfZQKBRRTbjBwJVWKY0GkTOahq9PXxwlDW2NE04IjZx9dAUi\nJc7/At71P9ewouKxgBBCXIwVPf8KGA8U+sW4TgixGRgFfBuhfikUio7GNHGuWYlvwEBMfy4/BCPn\nQI5zAKNPX5xFm9AqKzBTrbIHvXpZkXNXytiIiDhLKSsBhBBpWCJ9L5a98ZKUcrkQ4h7gfqyIujxk\n1wogo7XjZ2Ul43Q6jqlvublHX+Mi1lDXGB/EzTVu2wZlZXDuuQ2uaeVK6N0bhg9vNMlg6GD48nO6\nVR2Ggb0BGDnSeuvw4QRyc2MrJfRY/x8jlucshOgLzAGel1K+KYTIlFKW+d+eAzwLfA2E9jwNKKMV\nSkurj6lPcZeeFAZ1jfFBPF2j+8uFZACVYgQ1/ms6cECjpCSVadO8HDhQ02D7pG49SQXK12ygvoc1\nQGiVVkhj69am20czbUila/a9iAx9CiF6AJ8Av5FSvuxvni+EGO9/PhVYDiwFJgkhEoUQGcAwYF0k\n+qRQKDqHcIOBgTKhDfxmP8F0uuCgYEoKZGZ2rYkokYqc7waygPuEEPf5234NPC2E8AB7geuklEeE\nEM8ABVg/FPdIKWsj1CeFQhEhWiq/61xtjfyFDgauWxeYtt10hm4wna5xrrPBjh16aE2kuCZSnvNM\nYGaYt/LDbPsi0HxFeYVCEdVUVsKZZ6ZQUqIzcKDB559XBQXaNHGuWYWv/wDMzCx7n+C07TCRc19/\n5BwmnW79emsiSnoXqH7bdTK6FQpFRJBSp6TEkpJt2/QGq5XoxTvRS0vxhCxLBbB6tYO0NMjKalqJ\nwejRE9PlapJOF5iI0lUKIHWNq1QoFBHDsjIskdU00xZRgIS3/wnQYEHX7ds1duzQqaiwyvY2WRdQ\n1zF6n4BjZ+Nc565VOlSJs0KhOC5SU2HwYEuQTVPj/fdd9ntJb74ONBwMfOyxYCpcUVH4dQF9/fqj\nH9gPtcEhqK5WOrRrXKVCoYgoe/dqdOtmkJRk8tJLbvSvC8i4ZAaOXSUApDzxKK7CAvbu1fjvf504\nnVYUPGSIL+y6gD5/xoZjV9B3DkTOu3apyFmhUCia4CoswFVYYL+ur7fW4xw61ODyyz3s3KnzfvlZ\n1Pz0Z/Y2FU8+iyd/En/6k5u6Oo0HH6xj8WKaXYEoXDpdwC7Zs6dryFbXuEqFQtFuJD8xm+Qngkux\n7dmjYZoavXubXHedtTjrX//qIvWRBwCo/dGPSfhgDiUlGn//u4v+/Q2uvtrDhAk0uwJR6IooAQJT\nuFXkrFAoFCG4CgvIuOg83N8sxP3NQjIumYGrsMAu49mnj8GQIQZTp3pZutTJipIe1E2bTsUzL+AV\neTz9tJv6eo3bbqvD5Wr5XIZfnPWQjI3kZMjONtSAoEKhUITiyZ9EzU+utl9X3zwTT/4kSkossQx4\nwtdfaw3i/ZFfUXXPLAA2jfo+//yni0GDDH74Q2+r57I950Z1nXv1Mtm1y5qIEu8ocVYoFG0m8cNg\nufW0W26E6mo7eyJQ1vPcA28ynHW8o11BSZa1+vuTTybg9WrceWcdzjZMfTN6n4Cp600mopxwgkl1\ntUZ5eTM7xhFKnBUKRZsx3W4AvMNH4jh4gLQ7b7U94BNOMKGujtTHH2Gm4zm8ppOXX3axebPGv/7l\nZNgwHxdf3HrUDIDLhdGrd5Mp3IF0uq6wIkr8X6FCoWg3zDSrilrFM8/jOWUsie/8kz1LdgGW55z0\n6ks4infy/Z8lkZNj8Prrbh58MAHD0Ljjjnr0o1Aco09f9D27weOx2wLWSVcogKTEWaFQtJlAJOsd\nOIgjL76GkZXFbllFWrKXdLOc5KefwEhLx7x9Jldf7aG0VOPjj12cdJKP732vjVGzH1+fvmiGYQm0\nn660lmD8X6FCoWg39JJijOxsSE3F6NuPIy+8RLHZh/51RaTdcgP64cPU3DwTMyeHK67wAFakW1am\nUVV1dOey0+lKQnOdVeSsUCgUDTFNHCXF+Pr0s5sOjZtGOZn0820l4cN5+Lr3oPq6GwE4fFjDWqXO\ninTDTdNuCTudbucOu60rFT+K/ytUKBTtgnbgAFptrT17D2DfPKtWcz8su8NMTcW1ylocUAiDIUOs\nkqDNTdNuCTudLiRy7kprCUZsmSqFQhFfBEp4BuwGgJ09xgHQF0tAj7z6Jr68YYA1+2/+/Opmi/C3\nRnAiSlCck5IgJ8dQnrNCoVAECAwGBorhA3Yd5x4zTqbq9t+SMPc/DfZJTYWxY49emAF8J/RpcN4A\nvXqZ/injR3/MWEKJs0KhaBOBIkShnnMgxzn3+gupvvNuvCKv/U6YlISR272JOAcmopS1uhR0bKPE\nWaFQtImArREucg4M1NVfdGm7ntPXty/67l1gBP3qrjIoGN9Xp1Ao2o2A9xvqOe/eraFppj1Q1974\n+vRDq69H37/Pbguk08V7ASQlzgqFok04indipKZhZmTabSUlOj16mPhndbc7wXS6oLWhImeFQqEI\nYJroxcWWpaFZEathWNFrYEp1JAim04WKs4qcFQqFAgCtvAy9ssIWS4ADBzQ8Hs2uRhcJAv62XtJ0\nRRQVOSsUii5PIFPDCPGbG9dxjgSBzJDQus5dZSKKEmeFQtEqgXS2hml0wRVQIkUgcnauWWm3JSZC\nt27xPxElvq9OoVC0C+HS6AI5zgEPOBKYaemYDgfOjRsatPfubbJ7d3xPRFHirFAoWiU4ASVUnCMb\nObsKC8i4ZAaaz4dWU2OvWQiW71xbq1FaGpFTRwWqtoZCoWgV29bo299ui7Tn7MmfRGVON7LPnABA\n1b2z8I4bDwSj9V27dLKzI2erdCYqclYoFK2ilxRjJiZi5ubabbt36yQmmuTkRM5bSPhgDt7hI63n\nc96127tCXWcVOSsUilZxlOy0ChFpQTEsKdHo3dsMbWp3vHnD0KqqcH63FqN7D7u94Yoovsh1oBNR\nkbNCoWiZykr0w4cbpNHV1sLBg3pEc5zBqtVhZmUB4B05ym4PWCkrVuhUVka0C52GEmeFQtEijmZq\nakBkc5wDGFnZAOgho38ZGdaPwttvu5k+PTkuBVqJs0KhaBE7jS5MpkakI2cAwx85a6WH7bYjR4Je\nSlGR46iXwIoF4u+KFApFuxI+jc4Sxz59Ih85m4HI+XBQnEeMMNA069zHsgRWLKAGBBUKRYsEbY1g\nGl0gcg4MzEWSgK2hlQVtjdRU6NHDxDBM5s+vPqaVVqIdFTkrFIoW0Yut1a/DzQ7smMjZsjVCI2eA\n7GyTmhotLoUZlDgrFIpWcBQXYzqdGD172W2NV0CJJPaAYFnD6YCZmSYVFRq++MykU+KsUChaRi8p\nxuh9AjgcdtuuXRrZ2QYpKR3QgaQkzISEBgOCABkZVtReXt4BfegElDgrFIrmqa3FsW9vgzQ607Q8\n50gWPGqApmFkZTexNTL9C7KUlcXnLEElzgqFolkcu0uAhml0ZWVQXa1FtFRoY8ysbLRGy20HI2cl\nzgqFoosRLo0u4Dd3xASUAEZWFnp5GXi9dltmpnV+FTkrFIouh51G1y+YRheYHdhhtgbBXGctxGBW\nkbNCoeiy2Gl0YSLnjrQ1ArME9ZBBwUDkXFqqxFmhUHQxHC3MDuyIqdsB7Mj5cFNxVpGzQqHocugl\nxZiahnFCH7stsHZfx3rOgVznoDgHbI149ZwjMn1bCOECXgYGAAnAw8B64FXABNYBN0kpDSHEtcD1\ngBd4WEo5LxJ9UigUR4+jpNiafOJ2220lJRoOh0mPHh3pOfuLH4WNnDusGx1KpCLnnwCHpJSTgPOA\n54CngHv9bRpwsRCiJ3ALkA9MB2YLIRIi1CeFQnE0eL3ou3c18JvBynHu1cvE2YGVecLNEszIsB7j\nNXKOlDj/C7jP/1zDiorHAgv8bR8B5wDjgUIpZZ2UshzYDIxCoVB0Ovqe3Wg+H76QmhpeL+zZo5GR\nYXRoDWUzTNnQePecI/LbJ6WsBBBCpAHvAvcCf5BSBu6DKoAMIB0IvSkJtLdIVlYyTqejtc3Ckpub\ndkz7xRLqGuODTr/GDYcASBw6mER/XzZuBMOA775zMmNGGt9+y3EVHmrzNQ6yfiBSaipJCdknNRUq\nK52d/1m1wLH2LWI3JkKIvsAc4Hkp5ZtCiMdD3k4DyoAj/ueN21uktLT6mPqUm5vGgQMVx7RvrKCu\nMT6IhmtMWLOBdKAipye1/r68844LSAQsoV64sIqxY48ta+NorlE33eQAtXv2UxGyT0ZGCocOwYED\nVcfUh0jT2jW2JNwRsTWEED2AT4DfSClf9jevFEJM8T8/HygAlgKThBCJQogMYBjWYKFCoehkgnWc\ng7ZG6GrXHVnk3ghTcB+sjI149ZwjFTnfDWQB9wkhAt7zTOAZIYQb2AC8K6X0CSGewRJqHbhHSlkb\noT4pFIqjwLn8WwCMPsGiRytXOtA0k/feq2b0aKPjaim73RgpqQ0K7oPlO69fb5UNdRyb0xm1RMpz\nnoklxo2ZHGbbF4EXI9EPhUJx7Li+XQqAz5/jXFsLq1Y5GDXK4IwzOn5ZKDMrq8EMQWhYNjQ7u8O7\nFFHUJBSFQtEAV2EBGZfMsAoNARk/vgxXYQGrVjmor9eYMKFzqtt3tbKhag1BhULRAE/+JKrQcF86\nA4DK3z+FT+Sx9BnLN+gscTYzs9Cqq6CuDhKs6RANix913KSYjkBFzgqFoglJL/8fAPWTJpPwwRwA\nFi+2xHn8+E6KnLObTkSJ57KhSpwVihaorITly/UOnXARDWiVVvpX1W/uxSvyMAxYutTBwIFGh07b\nDiU4ESV0lmD8TkRRtoZC0QyVlTBtWjJbtjgYMsTH/PnVcbvSc2Mce/dgJiXhHT0G3BPYuF7nyBGN\nGTO8re8cIULLhgZi93guG6oiZ4WiGaTU2bLFupUvKnIgZdf4umiHD+HcsB7PuPF2waMlSzrXb4aQ\nsqGlTW2NeIycu8Zfm0LRBlyFBbgKC+zXQhgkJFhf/l69jA6bcNHZuBYvAsAz8XS7LSjOnRg5ZzYt\nuB/PZUOVraFQ+El+YjYA5fmT7DaPx3q87ba6LmNpuBYVAuA5/Qy7bckSB926GQwa1HkZEWZ2SwX3\nO6VLEUVFzoouj6uwgIyLz8f9zULc3ywk45IZuAoLWL7cgWFYEVl9ffxFZs3hWlSI6XbjOWUcYNVv\n3rVLZ/x4H1onfgzhyobGc56zEmdFl8eTP4m6Cy+xX1f+/ik8+ZPs1DGAI0fi78sfDu1IOc51a/CO\nGQtJSUCi7C8nAAAgAElEQVR0+M0Q6jk3tTWU56xQxCmJ770NgHfYSXZeb0CUoOuIs2vpYjTDoP70\nfLstWsTZjpxDBgRdLkhJic/iR0qcFQpA37cPsOpIeEUe9fWwbJmDlBQrMquI7wqlNq5F3wDgmdhQ\nnJOTTUaO7NwBUdO/9IlW2ngKt6kiZ4UiHtEOHbLLY+qlpdRfdCmrV+vU1mpMmWJlJ3SZyPmbhZgO\nB55TJwBQVgYbNjgYO9aHy9XJnXM6MTIywxY/UpGzQhGHuL4Jps9p/mI/ixdbiUznntuFxLmqCufq\nlXhPHm0vb/Ltt507ZbsxZlZWgzxnsCLnigqrbGg8ocRZ0eVxL/waAFPX0csC4myJ0lln+XA6zS4h\nzq5lS9G8XjynNUyhg873mwMYgbKhZjClL7RsaDyhxFnR5XEt/BozOQXvyJPRysswfCZLlzoYMMCg\nZ0+T9HSzS3jOrkULAfA0GgzUdZNx46JDnM2sbLS6OqipsdviNZ1OibOiS6Pv24uzaBP1p52O0a0b\nmsfDhpX1lJdrTJxoCVJaWtewNVyLvsHUNDzjJwJWcf2VKx2MHNmBK560QkuzBONtUFCJsyKmqKyE\nJUtotypxLr+l4ck/EzPDCsGWLLB85okTrcf09C5ga9TW4lqxDO+IUfbn0NnF9cNhtDBLUEXOCkUH\n0LhUZ3U1LF2qc/rpKUycCNOnJ7eLQNviPOlMTP/98eIl1mBgIHJOTzeprtbwdl5ZiYjjWrkcra4O\nz2nBehoLF1p+88knR484m2FmCcZr5KxqayiijspKmDIlhZ07dZKSTDIzTfbsaRhHFBU5uPPOBG64\nwcOIEQZVVVYVOSGO7hbcvfBrjIxMvCNGYWRmYgKLV6fSvbvBwIHWlz4tLZjr7K9aGXe4vvH7zf7B\nwMpKeO45qyLdH/6QwPnne6PC2jDsms4qclYoOhwpdXbutP40a2o06uth0iQvP/5xPbkZdQDousm7\n77qZOjWF009PZty4FM4/P+WoImq9eCeOHdvxnJYPDgdmZhZbGMTe0kQmTgzWkUhPtx7j2doITj6x\nIue5c51UV1vXu22bHjXlUs0wswTjVZxV5KyIOoQw0PFh4GDQIB+ffhoscu/Y/AOK6geR8ebjLFrk\nZM4cJ/PnO+3CREVFDpYv15k8ufXZbIHyoJ4zrCp0RmYWBVjPTzsteCufnm59+S1xjq916gBcC77E\nteQbvHnDMHNyqKmBZ5912+8PGeKLmnKpoQX3A8Rr2dDo+DlUKPy4Cguo/f41GDg4h09YuaMb/U7p\nT/bQ/nQ7IYfsJZ8yYeVfGHzhWC5N/JC//a2WZcsq6Z5Zax/j5z9P5umn3ezb1/ISU+6CBQDUnzEZ\nADMj0xbn0EGwgDhXVMTXlz9AyoP3WX6zP2qePTuBzZsdXH11PR99VBVVK8DYxY9CBgSzslSes0IR\ncYzuPVixuxcA5/MxSb3SMXNyMHNy8PXsaW/n3FxExv+7mrRf/oK+m79mw9AL+Wz4Tdx1Vy0ul8ns\n2QmMHp3avNVhmrgKCzBycvDlDbOaMjP5mjPJSKhh2LBgpBjwnI8ciey1dzSuwgKrPOraNdbrbxay\n9P/W8de/ujjxRIMHHqhj7NjoSaOD8GVD/SU34i5yVraGotMJ2Av6rhLS7vw1y6sfBGDEZYOpG/Bj\nqu+4C4Dkxx+lDkipr6Z+2QocJSUkvv0miW+/CcBUPmNSxhp+8ex93P3hFN54w7o1DywxNXZsUHAd\n27bg2L2L2osuBd2KUXZ7c9nCYM7LXYPDMdDeNl49Z0/+JKo9Htz+wcDdDz/PjbdPQNPguedqSE7u\n5A6GwQwzIKiyNRSKCJH82MM4t25BP7AfIzWNJT0vQt9vMvTxn+L9fI69nTdvGPUXXUpKbho1f3ud\n+gsuxrVkEUnP/ZGET+cDVi3mJJHHQ6fV8emnTvbv1+nevekSU64CfwrdGWfabYu2WBF7fsYaIFSc\n49TWME3Sbp8JQN1532PWw6ns3Kkzc2Yd48ZFh8fcGDM9A9Ph6BJlQ5Wtoeg0XIUFZH5vGu4liyxh\nTkmldPbTrDoyCCEMUlKg/qJL7e2bPNd1PKfl4x15MqbTidGtm12LOTUVXn3VmuI7eXLTNDBXYVNx\n/madlec8KfHbBtsGU+ni68uf+NrLOHbuoG7adP5z9du8smY8J53k4/bb6zu7a82jaZiZmV2ibKgS\nZ0Wn4cmfZE8VBij74GPWjvgR1dUaY8a0feKD96TheCaejn7wIL4+fe320aMNkpJM1q1zNNzBNHEv\nLMDXsxe+QYPt5m+WJuCmlrz6NQ02j0fPWd+xndRZ92JkZCLv+DM33pSE02ny3HO1JCR0du9axsjK\n7hJlQ5U4KzoV9+efAFB9zfUkfPxfVq2yhHTMmLbfVtdfdKkt8ma3bna70wmjRvmQUqeqKrh9wltv\noB88gCd/EoFk5t27YeNGnXoSmbLxxQYDiHHnORsGab+6Ca26ir2/e4opVwzk8GGdjAyTAQOi084I\nxczKtsqGhlSmi8eyoUqcFZ2KdugQRmYmVY8+jlfksXKl9Sd5NJEzgGfCaQC4li5p0D56tIFhaKxd\nG4yek//4B2ufSZPttjlzXIAlvhs9gxtMuog3zznxlRdxFxZQd973WDPsckpLrWs9dCh6Jpu0hJGV\nhebzoVUEb2XisWxo9P9PKOIWrawUx4H9eE8eA5pG/UWXsnKlg4QEs0EqW1vwjjsVU9dxLlnUoD0g\n8qtW6XbqmHPbVgASX3/FzhQpKQl+FfLYgBDBH4egrRH74uz+19uWnZGVRcUTfyQlNRh9RtNkk5YI\nLvQa36twK3FWdBrOVSsB8IwZC1glejds0BkxwjjqJZHMtHS8w0fiWrkc6urs9tGjA+LswJM/icqH\nHrPfq/jT85a1gbXih8tl8unY2/mWU0kj6GukpIDDEQeV6QyDtN/ehlZXR+XsP2D26GGv+HLjjXVR\nNdmkJbpK2VAlzopOw7VqBQDe0acAsG6djtd7dIOBoXjHT0Crq8O5epXdNnCgVThp5UrL1kh+4VkA\nPKeMtTM7yspg7VqdU0/1ccbAElKpahCVaZpV0zmWC+67CgvIOut0dL8VELhr+OIL63P52c88MSHM\nAGZ2uMg5/qZwK3FWdBrOlX5xHmOJc2AwMBDtHi227xxibWiaVfJy2zad0lLQDh4AoOq+B/GKPMBa\nkso0NU4/3Yfhvz/W/MtVBYj1ms6e/El4/TMhwcoHrzp1EgUFTgYNMhgwIHZqhqjIWaGIMM5VK/B1\n74HR05r8EYhuTznlGMXZn7Hh+nZxg3bbd16p49ywHiM7G8+E0+y86cJC69Y+P9+HGfjilzcU57S0\n2BZnTBP3F59hutxU/fpOEj6Yw9KlDqqqNM4+O7YKVQcj5/guG6rEWdEp6Pv24tiz24qa/elsK1c6\nSEszOfHEY4vijN4n4OvXH9fSxWAEB7ZGj7aer/lwL459e6mbPsPKs/NTWGgNQo4d67ML7oeLnCsr\nYzdVy7FtC3p5OfXTplP923vxijw+/9z6DKZOjS1xNsKUDQ0UP1LirFAcJ7al4feby8thyxad0aN9\ngVIXx4Rn/ET0w4dxbC6y2wKR+OqCagDqz7/Afq+0FL77TmfcOB+JiWD4l2hqHDkHcp3ba3msjsb1\nxWcA1E+dZj1edClffOEgMdFsUB41FmipvoYSZ4XiOHGuWg6Ax+83r14dmHxyfEJhWxshvnPPniY9\nexqs2JmLmZxC/eSz7PcWL3bafjNg2xqhg00Q++l07s8/BaD+7HMA2L1bY8MGB6ef7iMpqTN7dvSE\ni5wDtobKc1YojhNXIHI+2RLngN8csCCOlXCDggBjBpez29eT7adfRqgaffONdd78fEucm4+cY1ic\na2pwf7MQb94wjBP6APDll5alEWt+MwQHBBtGztajipwViuPBNK3BwH4DMHNyAOyZgcc6GBjAJ/Iw\nMjKbiPOpuhWpLx70Pw3aFy60bu0D57VvmcN4zhCbswRdiwrRamqoP+scu+3zz60fpVjzmwFIScF0\nu1W2hkLR3ug7tqOXltqWBlhpdN27G/TqdZwpXbqOZ/wEHDu2o+/bazdPKH4PgKV6sNBSaSmsXx/0\nm4HggGB5Y1vDeozF4kfuLxv6zR4PLFjgpF8/45gHXzsVTcMI1NfwE49lQ5U4Kzoc12prZmBgMHDf\nPo3du3XGjDHsRVWPh4C14VxqpdTpxTuZuO1tAFauD1aQX7Sood8MIbZGM5FzLNoa7i8+w0xOtj+X\n5csdVFRoTJ3qbZfPuzMws7KaVKaLt7KhbRZnIYRTCDFSCH/mvkJxjDSefHKsxY6awzO+oe+c8PF/\nyaaUgTllrF7tsIuZFRZat/ZnnBFy3sREzMREtLKGkXOsirO+cwfOok3Un3EmgVqggVmBseg3BzCy\nstHKywnNbYy3sqEtirMQ4iP/4whgI/A68LYQYq2/TaE4apyrVmBqGt5RJwOhg4HtI87e0WMw3W5c\nS6zI2f3hPExNY8x4B2VlGtu2WV/gwkLLb278o2BkZDaJnAPZGpWVsfXldwdS6M6eZrd9/rkTt9u0\nB0FjETMzC8000UIGbuOtbGhrkXMP/+MfgV9KKcdIKU8Gbgb+FtGeKeITnw/n6lX4hgrMVMvIbW9x\nJjER78ljcK5djb5zB65FhXjHnsro06xqSqtWOTh8GNavd3Dqqb4mxeXNrKwGX3qIXc/Z/UXDFLp9\n+6zyqRMm+GKmlkY4jOxAOl24QcFO6VK709Y1BDOklB8FXkgpFwghWl3+UQgxAfi9lHKKEGIMMA8I\nzA54QUr5thDiWuB6wAs8LKWcd3SXoIglHJuL0Ksqqff7zaZpieWAAQb+71u74JlwGq5vl5Ay+yE0\nw6BuxoV2mp5VltTaLlz0aGZkom2S1ixD/4yYmLQ16utxf70A76DBGAOsNRG//DL2LQ1ovWxodnYM\nDnQ2ojVxHiyEeAGoE0JcK6V8UQiRBVwD7GlpRyHEncBPgcAaFGOBp6SUT4Zs0xO4BRgHJAILhRCf\nSinrGh9PER84V/onn/jFeds2jbIyjZNP9lFZSbtFc54Jp8FzfyTxvXcAqJtxASN7+NB1k1WrdPvW\nN3QwMICRmYlmGGgVRzD9A4SxKM6upYvRqqvsqBmC+c1Tp8b2vX/rxY/iX5yHA6cCZUAvf9uPgQnA\nz1rZdwvwfeDv/tdjASGEuBgrev4VMB4o9ItxnRBiMzAK+DbM8RRxgF0m1D8YuHSpFcktWOBk+vTk\ndqsp7Dl1vP3cO+wkjBMHkQIIYbB2rYPSUo2kpKZ+M2ALslZW1kScYynP2Z4V6E+h8/ksce7WzaBP\nn+gvqt8SXaFsaIviLKUsBoqBf4e0PQc819qBpZTvCSEGhDQtBV6SUi4XQtwD3A+sAkIdogogo7Vj\nZ2Ul43Q6WtssLLm5ace0XywR1de4bjW4XGRNOR0SElgVLL1MUZGD/fvTGDiw9cO0eI1ffQWzZtkv\nnVWV5H63HKZM4bTTYMMG2LTJwdSp0KdPmOP06g5Aju4B/3lycqz6TDU1zg77fI/7PF9/AYmJZF50\nPiQl8cUXVu1q0JgxI41vv22/O5Vj5ZivsX9vANI91fb/UV//2r6mmUxubnv0rn041mtsq+fcBCHE\nLCnlrKPYZY6UMjDKMgd4FvgaCO15GlaU3iKlpdVHcdogublpHDgQwxXT20BUX2N9Pd1WrcJ70gjK\njtQD9ezblwhYA3VDhvjo3r2aAwdaPkyr1zh8LI6HHif7zAkAlD0wG8/wsXCggrw8F5aDBuPH13Hg\nQH2T3ZMTUkgByrbtwtN3iN2elpbKoUMGBw4c29/f0XC8/4/67l3krF1L/dnnUF7phcoKXnklAXAD\nsHEjLFxYxdixnRdBH881uhxJZAJVxbup9h/D4XACSezcWcuBA5726+hx0No1tiTcxzMJpUXPOQzz\nhRCBe82pwHKsaHqSECJRCJEBDAPWHUefFFGMc8N3aPX19uQTgG3bdJKSTD78sKpdl0lK+GAO1bf8\nmpqr/hfX+uCfVKiN0VxetV1wP0x9jVixNZJefAGggd+8YYNOwIuNlfUCmyNQ/Mi5/ju7LVj8KDb+\nj1rjmCNnKeVfj3KXG4BnhRAeYC9wnZTyiBDiGaAA64fiHill7bH2SRHdBNYM9I4eA1ge6NatOkOH\nGowb175C4c0bZhfTd/uXowLo189A00xMU+PuuxP45JOmPwgBn1kPU5lu167YmFSb+NYbQNBvPnLE\nyooZPdpg9uxahDA63dI4HgI1UFzfLrXbAgOCpaVdQJyFEH2x7Ie+WFbEbCmlz//ePCnlBS3tL6Xc\nDkz0P18B5IfZ5kXgxWPpvCK2cM//EAhmapSUaNTWagwe3P4RXECYGz/fulXHNK0v7+bNDqTUm9za\nt1Rwf+PGBhl2UYersIDkxx9FP3QIgNTbZlJ9x10UHjkLn8+ast2ZVkZ74CosIPn3jwCgHzpIxiUz\nqL7jLjJ7ngnET55za39iLwPvA9dhZWjMFUIEBP2ESHZMEX+4v1mIqev4/BUANm+2/vyGDOk4sRDC\nYMgQn/+84W/tjYzwS1Wlp4NpalRVNdklavDkT6L2iivt15W/fwpP/iS++soaQJ88ObZT6MC6xsrH\nn7ZfB64x3sqGtibOOVLKV6SUy4GLsDIr/hH5biniCVdhARkXnYdWXY1mGGT88CJchQUUFXW8OKem\nwvz51Xz0UfMed3NlQ2Ol4H7S318FoPYHl9srjH/1lZPUVGsprngg4YM5mImJGN262dcYb2VDWxNn\nrxBiOICU0gSuAnKFEH/hOPxqRdfCkz+Jmmt/Yb8ORDoBcY6ErdESqakwdmzznmugMl24AUGIfnHW\ni3diJqdQ8cc/4xV57NihsW2bzhlneHG5Ort37YM3bxhGt1zMpGR7FfV4KxvamjjfCswTQlwJIKX0\nYEXQPYGTItw3RRyR+O9/AVA3dZod6WzerKNpJieeGF0eaMBzbjwgGAvi7NhShGP/PuqnnA0JCdRf\ndCkLFlhx1JQp8RE1gzWOYKakoFVVNhhTiKeyoa1NQikEBgoh3CFtVcAlQojRke6cIn4ITKatufEW\ne3mhoiKdfv1Mu9B91OB2YyYnh4mcrceKKE0jB3DP/xiAuunn220Bv3nKlNiup9EYMzUVbfu2Bm0Z\nGSbFxVE6WnuUtNWaGCiEuA7IatT+83bujyJO0fzq7B2ah9mjB6WlcPCgzpgx0SkYLZUNjebI2f3p\nx5iaRv3UcwHweqGgwFr1ZODA2K83EYqZnIpWV2ct7eL3azIzTdavt8qGOo5tEnHU0FZxngO8BayJ\nYF8UcYyjSGJkZmJ2t6ZGBzI1OtpvbitmZhb67l0N2qJdnLXyMlyLv8F7ylj7c161Sqe8XOPiiz0x\nu+pJc5gpKQBoVZX2qumhZUPbs8phZ9BWcS6TUj4Y0Z4o4pf6ehxbt+A9ZRwBheiMNLqjwcjMxLFx\nPaEhWLQXP3J/8Rmaz0f9tPPstq++sr7i8ZBC15igOFfZ4hxPZUPbKs6vCiEeAT7HqrsMgJTy64j0\nShFXOLZuQfP57FF1oNMyNdqKmZFprbRxpNyuHRztnrP7E7/ffG7Qb16wwIGum0yaFJ320fEQWKxB\nC0k8bziFu2uI8xSs0qGnh7SZwNnt3SFF/OEokgD4hgq7Ldoj59BZggFxjmpbw+vF/fkn+HqfgG+4\ntYJcRQUsW+ZgzBjDjijjCTtyrgz+WsZT2dC2ivM4KeWQ1jdTKJrilBsB8IaIc1GRg+xsg5yc6Ixu\n7FW4y8sI/HxEcyqda9lS9LIyai7+gW0dLVzoxOfT4i5LI0CorREg4DmvXKlz6qmxvRRXW3NO1goh\nRkW0J4q4xbHJEmffUMvWqK+H7dsjU1OjvQg3SzCaPWf3fGsVufrpoX5zIIUu/vxmADPFUt5QcU5M\ntP6PHnsskenTk6ms7JSutQttjZxPBFYIIfYCdgFcKeWJEemVIq5wSomRkopxQh8Atm/X8fm0qLU0\noGHkHCAQhUXjIq/uTz/GTEqiPv9Mu+2rr5ykpZmcckqcinNqQJyDChw6AaWoKHxhq1ihreJ8BfA9\nLI/ZC3yINTioULSM14tj62a8Jw23b7ejfTAQQjznkFmCDgekpppRZ2vo27bi3CSpO28GJCUB2FO2\nzzvPEzdTthsT9JyD4hz6gx/rNavbamvcg1X68/+AV4HzsBZmVShaxLFzO1pdHb4hsTMYCCHiHEUF\n9ysrYflyvcmtesKnVpZGaApdPE7Zbkw4W6NbN8vWuPRST7su3tAZtDVyniCltPOghBBzUSuWKNqA\nQ1qZGt6hsZNGByG2Rpiaznv3dvz04NWrdWbMSMbj0Rg82NdgkQD3J/MBqJ823d7+s88sv3n8+Pgc\nDITwtkZysvWYlmbGtDBD2yPnYiHE4JDXPYBdzW2sUASw0+hCcpw3b9Zxu0369YvOTA0IGRAsbzyF\n20pRMzu46++848TjCS4S8N//WnGV+9OPcRV+jefkMRg9e7Fvn8attybw8cfW+9dfnxTTg2ItEc7W\nSEmx/mOqqqLLejoW2ho5u4DVQoivsTznM4A9QogvAKSUKt9ZERY7jW7IUMAStaIinRNPNHBGcdFZ\nu+B+mMjZ57MK7kcqMnMVFkBmMgwfa7c1tlJmzkxk27Z6Hpr3EJrPx4HJF/OH2W7++lc31dXxMyjW\nEuFsjYA4V0d+Dd6I09avx/2NXv+hvTuiiE8cmyRmQgJG/wEA7N+vUVER3Wl0AKZ/WQ2tLHzZ0IoK\njdTUyITPyY8/Ci4HvDvPbtu+3Sqv+v771ZSVadz1a42nnkriY94kn0Lee+5yDhsJ9OhhcPfddbz6\nqovNmx0xPyjWEqG1NQIEbI0uEzlLKRdEuiOKOMQwcBZtwjd4qF2fojNWPzkmXC6MlNQWV0Pp1at9\nxTmwNp578TcAZJ+cR9Xtv6Xupz9j82adgT2rmeRbgJnlYkafR7jj4E95hWtYzwh00+SOO+q46aZ6\nkpPhyis9SKnH/EKuLRH0nIORs9sNLpfZ4O4hVomPwqeKqETfVYJWXYV36FC7LRYGAwOYmZlh1hEM\niHP7n8+TP4ma62+yXzv27Cb9tlswJ53HwYM6eZXLSb/mKrIuPJecVQu4pu8n9raGqXH22V47cmxt\ntZd4wExuGjmDFT1H8zqPbSWKXT9FrONsNDMQYiONLoCZmYW+c0eDtmDxo8hEZonvvW09mTaN2pR0\ntLo6Ns+3rJVhFUvROYSRmkbV3fczIL0XQ/7ko6jIwdCeZQgR4wWMjxaXCzMhoYk4p6TER+SsxFkR\nMRybNgGxl0YXwMjMxPndWqtivX/0MtLFj2yj5M47qduxm/qLLmXZi3VwD+Rh/diVffgZvrxhuIH5\nM6r99oUjrqPk5jBTUxvYGgDJyfGxjqASZ0XEsGtqNEqj69UrNm63TXuh13LMnBwg8uKsGX55Hj6c\n+pMnAFC0xyqN2f9H46jqk0vC3P9QnTcMCNoXXRUzJbVBKh1ASgrs3h374qw8Z0XEcMqNmE4nvoFW\nCZaqKigp0WMiagYrcgbQy4MZG5H0nAEccoN13p497baAFdT3/p9QfefdDepid3UCi7yGkpxs2RpG\nbPyZNYsSZ0VkME0cmyS+EwfZ67tt3Ro7fjOERM4NKtNZj5WVEYjMamtxbNuKTwwjdE2pzZt1srJM\nu7xq6GrTXR0zOaWJreHPsKOmphM61I4ocVZEBH3/PvQj5Q0GA2Mmjc5PuLKhkbQ1HJuL0AwDrxhm\nt3k8Vo5zrNxtdDRmaiqaxwN1dXZbcnJ8zBJU4qyICA67wH5sptFB+LKhkSy475QbAPDmBX/Qtm/X\n8Xo1hgyJ3wJGx0NwlmDoFG7rMdbT6ZQ4KyJC4wL7EFtpdBC+bGgkPefAD5ovJHKOtR+0jibcaiiB\nyDnW0+mUOCsignNT02p0GzfqJCSYtsBFO+Ei5zQrcSIiec7Ojf7IOUScY+0HraMJN0swWPyoU7rU\nbihxVkQExyaJqWn4BlnFDI8cgU2bdOrqtJhZPih0kdcATqcVmUXEc5YbMLKzMXNz7baAOKvIOTy2\nrRGyyGtglqSKnBWKMDg3bbSKHflX5liwwIFpBlZCsSqlRTtGZviyoenpJhX7a63qce1FTQ2O7dus\nOw0ttKqcjssV3eVVO5Nwtka8lA2N/m+IIubQDh1CP3iwQT6uL2Q8K1YqpQUi53BlQysOekh58HdN\n9mlutZLWcG7ehGaaDfxm07Qi54EDjbhdaup4CS/O1mOslw1V4qxod5yBAvshS1Pt3GnVfbj//tqY\nWT4omOccHBB0FRaQtWs95b4UnCuXk3VWvh1BV1bCpEkpnH9+ylFbN46NTTM1DhzQKC+P/vKqnYmZ\nag0CNLQ1VOSsUITF/eFcALxDg+K8caP1p3b++d6YEGYAHA6MtPQGkbNn/EQytCN4cVFDEvr2bRhZ\n2QB89JGTXbus6zxa68YZJlNDDQa2Tku2hoqcFYpGJLz/b6BhTY1Nm3QSE036948t79TMzGzgOac8\n+DsyK0sA2D/1MvSqSjJ+9H30kmKWLw9WhUtNNY/KunHIppkagTS6QYOUODdH+FQ661FFzjFCZSUs\nWUJMZAnEKq7CAjIumYFjzx4AUn93N67CAgzDEpohQ4xAzf2YwcjMsrM13HPfJ/mvfyY9yQPA7gef\np+ayH+HYu4eUKy5j7vsOMjNNhg3zUVmp8dZbbTeKnRs3YOTkhM3UUJFz89i2RlXTdQRVtkYMUFkJ\np52WwsSJxEwaVyziyZ9E5WNP2q8r/vAnPPmT2LFDo6ZGY+jQ2BMZMzMTvaoSx8YNpM28ETM5mcSL\npwJWemDln/+P6utv4oui/hw45OCH47fy7m1f0a2bwf33J7BsWRu+YtXV6Dt3NIiaQaXRtYVwi7wG\nI+fO6FH70SXEWUqdffuOzQtUHB2Jb70BgHfQYBI+mANYlgZAXl4MiozHC0DGT69Ar6yg4slnSOlv\neU+hOmYAACAASURBVMyBXOeqBx7h1T53A3DN4l8w+G/385e/1OLzwbXXJnHoUMsRnLNI+jM1Glab\nKyrS6d7dwL+coSIMdp5ztUqli0msddSs/7CBA42YSOOKVczERADqLr7UTqWT0vIyYjFydmzdbD3u\n2E7N//4/6n5weYNFXgGOVOrM3XcaQ/UiJhz5DPeiQi58ajp3/WgTu3bp3HBDYoNUwibnCDMzsKYG\nios1ZWm0QkuLvKoBwRggNRV+8pN6AGbPro2dbIEYJJAb7D1phF3aMnCnIkTsFO+x/fP9+wAwUlOp\nO/8CoGllurlzXdR6HFz2E51ArOY9aTi/fKo355zj5auvnNx+e0KzdpqdqZEXOhgIpqmpwcBWsKdv\nVzb1nFXkHCMEbqn37Okyl9wpONd/B4Bv2HC7TcrYy9Ro7J8feeUNPFPOBoI1nQPFj955x1pQ6McJ\n71J9w80Y6ekkv/RXkt/6O48/XoPTafLGG25OOy0lrECHy9SQVqq4ipxbIbjIa9DWSEgAXTdV5Bwr\nnHiiJQxbtsT2r2m041j/HWZior36SSBTY/Dg2MvUSPhgDlW3/5aq23+La+liuz20bOjOnRqLFjnJ\nz/fSe0Ivqh54lLKPv8RITSX1tls4PHcpXq/1N7dvn85DDyVgNvqNcsqNGN1y7aWwADZawbQS59Zw\nODCTkhrYGppmzRJUkXOMMHCg9UceWI1DEQG8XpxygxUB+hdE3bnTytSIRZ/fmzeM6jvvbrI0VECc\nKys13n3XSpe7/HKPbeP4Bg+h/J3/gNvN+Nk/YmjuIQCcTpNXXnFzzz0JQQ+6shLHzh148xpmagTE\nWWVqtI6ZEn6RV5VKFyN0726SlgbbtnWZS+5wHFu3oNXV4T2poaUBxKQ4hy4HFfo81HN+5x0XSUkm\nF1zgbbCvd9x4jrz4KqmeUpYdHsTCoVfz9ddVDBvm46WX3Fx3XSK1tSFT3RtlamzcCImJJn36xI4V\n1FmYKSlhF3mN9VS6iK6+LYSYAPxeSjlFCDEYeBVr9fd1wE1SSkMIcS1wPeAFHpZSzotEXzQNhgyB\n9et1DAN0pdHtjnP9OgB8DcTZ8jJiUZybI+A5FxQ42LVL5/vf99h1nkMxU1LxDRhI2pbN5G96Hc8t\nG/nw7of4nz+fzdy5Lvbv17hrbAVTScEM8ZsNwxLnE0801N9pGzBTUtFLixu0paSY7N8f2x9exHov\nhLgTeAlI9Dc9BdwrpZwEaMDFQoiewC1APjAdmC2ESIhUn4YMgdpajT17Yvt2J1px+AcDvSeNsNti\nMVOjNQK2RqCOxuWXe8Ju58mfxJFX3rBfmz4vKVNP5Z13ajjvPA9Llji55PkLOYUVlPcPfmZ79mhU\nVyu/ua3YK3CHmPnJySZVVTTx92OJSP60bAG+H/J6LLDA//wj4BxgPFAopayTUpYDm4FRkerQkCH+\njm2J7V/UaMW5wS/OIZkamzZZq5/EUqZGa7hckJRkXU+PHgZnntn8D09gUNE7eAjulStI+f0jJCbC\nL39Zb29TxFAWlAb/7NXMwKPDTE1F8/mgttZuS0mxUhFDmmKOiNkaUsr3hBADQpo0KWXgG1oBZADp\nQHnINoH2FsnKSsbpPPqh/4A4HziQTEgJg7gjNzfMPXZHsHE99OpFt2EDgUCmBuTlQc+e7dunTrtG\nP2lp1kSRyy/X6dWrhb6MPwUuuwzu+Q3k5ZH8pydJnjqZM8+6kLy84MDffb/vzqTzoV8/2LvXahs7\nNoHc3IjdSEYF7fL/mG3l1ucmaeA/nn/hdJKS0jr9u36s1xhRz7kRoWFAGlAGHPE/b9z+/9s78/Co\nyvPvf845M5NMJoGwCooICB5AUJCdEKDsoKDw/nzdqta9tVr0p9Z9o3Wr0qqVtop7pbWvuICVJYIY\nQkB2EAQPIDuihD2Tbbbz/nFmSSDsSWbOzP25Lq7MeebM8Dwzc75zz/3cy3E5cOD0AhgvuMD6r1av\n9lFUVHGCs+1JkyZZFBUVn/jEGkY5fIjG27bhGziIQ+H/f9s2hdLSTM4/309RUc2ZMPFaYwSvFw4c\nyAQUpk0Lce+9JcdObBo4AoqKAQ3tXx/T4NIhmNffQMWc+cz8qDE/db6CqeeMZ+KWa+nXL8THH5ey\ncqULcHHWWSUUFSWv9VxT72OWI410YN+2nwiFvagORzrgZPt2L9Y2V3w40RqPJ9x1+ft+pa7rA8O3\nRwIFwBIgV9f1dF3X6wMdsDYLa4WI5SwRGzWPtm4dUL2/2ZY1NY6DYaj4/da+xfbt6knXagl2vgjv\n8xNRDx2k3i03kL15Nb1ZwoRRBTz0UAU7dqhcfnkGCxdavwrbtEmu1622OF4HbjvHOtel5XwfMFnX\ndRewHphqGEZQ1/VXsYRaBR41DKPWvESNGkF2tsnmzfZ9wxKVSKRG5TC677+3b02N46HrIdq1C7Jx\no3bKLbfKr70ex5JvcP/rn2Td9ivAKrD/vzf4cLlMJkxIZ/duaNrU3ptZdUmsG0p1KdxxmVKNUKvi\nbBjGVqB3+PYGYEA150wGJtfmPCrTpk2INWtUAoFonoRQAziqidSIVaNLnkgNsGq1zJ5dimGo4aJa\np/Z473Mv4Vy9Csd3a4BY2vZdd/lRFHj66XT27LHK29qlpVc8OX7xI/saYin3+7516xB+v8LOnfZ9\n0xIRx7q1mA4HwXYXRMcMI/kiNSJkZkK3bqcuzADOFcswXa7Yc/3hiWgfwt69Y19kUt725EjWDtwp\n985HqnxJGncNEgqhrV9nCXNaWmTItjU1aht/Ti7Fr/wtelw88VX8OblAzGUC9ulSHm+qb/Jq/bVz\n8aOU+2Ef2WSxNgWT6+d2vFB3bEct8eKrFN+8Y4dCaak9a2rUBZH458jt0gceBmIukz17smjaVFwa\nJ0OyWs4pK85iOdccx/M3izhXT6B9h2i9Dle4Y0yEzExo3RqKiuIxM/txvCavdracU06hIuIsWYI1\nR6ymRsfoWCRSQ8S5eo5VVEk4daKtqkpibo1ksJxTTqHq1YPGjUNiOdcgx7ecxXUk1C7RbijVxDmL\n5Wwz2rQJsWOHgr/6ejXCKaKtW0soO5tQ87OjY8kcqSEkFtX7nK2/YjnbjDZtTIJBq4uFcIaUlqJt\n/sGymhXr9QyFLMv5/PNDEksu1Doxt8bRSSgS52wzZFOw5nAY61FMs0pm4M6dVqRGsqVtC4lJyHN0\nk9fIhqCdMwRTUp1kU7DmiDZ0raamRrKlbQsJSliJqwulE8vZZkg/wZpDi9RwrmQ5r1ljva7nnSfi\nLNQBqoqZ4akizm43KIoplrPdEHGuORzrvsNUlGh9CK8XJk2ysgSffz6NI1q7CUKtYPURjIXSKYpl\nUMuGoM3IzIRmzUJSOvQMcS6Yj2P1SoKtWke3x9esUSkuti6IbdtOvpymIJwJoczk68CdsldOmzYh\ndu60dxubeON5dgJqcXEVf/OqVbFCGlIbQqgrTM/R4mz3DtwpLc6mqbB1a8q+BKeNs7CA+leMwrls\nCQCOb1fhLCzA54PJk12kp5v8+9+lUu5SqDuO0eRVLGcb0rq19SaK3/nU8efk4n1+YvS49Dd348/J\nZepUBzt3qtx4o5/Bg4MizEKdEcrMRDHNKimBEcvZrk0LUlaZYrHO9v1mjSfpH07BdDgIZWah7i0i\nEIBXXknD5TK5807fiZ9AEGqQWCJK1RTuYFDBZ9OPY8qKc6Sus2wKnh7als0ogQAljz5BoOOFTJvm\nYMsWlWuu8dO8uU1NFcG2VNcNxe6tqlI2ubZVqxCKYopb4zRQDuzHOf9rgk3PovzaGwiluXl5gAtN\nM7n7bpuaKYKtiYpzNVmCpaUKDRvaz2BIGWVyFhbA119Hj9PT4ZxzTMkSPA3cb/wdtcRL2W/Hg9vN\njBkODEPjyisDtGxpv4tAsD/RbihJVHA/ZZQp48Xn4Kmnqoy1bh3ip59U2/7siQfK4UO4J/+DUKNG\nlN1wE6YJf/mLC0UxGT++It7TE1KUqOVcWp3lHI8ZnTlJL86RsC/XwgWQn2+FgIWbaVZtWSWcDO43\nX0c9fIjS39wNHg9z52qsWaNxxRUBzj9frGYhPiRjq6qkV6Wjwr5+Oz7aTDOyKTh3riZpxieB4i3G\n/fokQtnZlN98G14vTJhgpWqPHy++ZiF+xJq8Vlc2NC5TOmOSXpzBaqBZMeJSANyvT4qOn322Jc7P\nPJPO8OEZItAnIP2dt1APHKDs9jspJot+/Tx8/72Gx2PSsqVkAgrxo7pojVjZULGcE5ZA+w4UvzIJ\nNA1tx/bouFLpPdu4UZM6EMfBOfdLMl6ZSCirHmW3/ZpvvtH48Ufr9SopUeS1E+KKuDVsim/MWMwG\nDWHAABxbNqPu/hGAX/wiiNNpvYFt20odiOOR9fD9qIcPUXbr7QQys3ntNVf0PqmhIcQbM8NKQlGr\nDaWLx4zOnJQQ5yhjw63oZ34BWNXpfvUrq5Hgww9XSLpxNTgLC6g/ejja1i0AuBYU8JfxP7FwoYMh\nQ/zMmFEiNTSEuBNp8kq1SShiOSc+l18OQNqM/1YassR53ryUzcc5Lv6cXIItz4seT7/6PV78qC0t\nW4b429/K6d49JMIsxJ3q3BpiOduJc8/F36UrzoUFKAcPANCtW4jGjUPMmuUgGIzz/BIQ56JC0j/6\nkFCDhmy45Q/c8VgLnE54880ysrPjPTtBsKiutoZYzjbDN2o0SiCAK28WAJoGI0YE2LtXZdky7QSP\nTjFKSsj63W9AUdj73kdcv+Yh9pV5mDChgi5dxMcsJA4Rt4ZaqRtKRoaE0tmKilGjgaqujZEjAwDM\nmiWujcpk/vFJtG1bKbvrHh77vB9LljgYPdrPTTf54z01QaiK242pKEdYztZfsZxtQvACnUDbdrjm\nzYl+pebmBsnIMJkxw2Hb2q81jXPBfNxvvUFAb8+SSx9l8mQrOmPdOkl3FxIQRbFcG0nUgTvlxBnC\nro2yMlxffwVYRZAGDQqwZYvKhg0p+ZJUQfEWk3XPbzE1jeJX/85H02M7fj/8IPHgQmJiejxV3Bpu\nt/XXrsZESl5lFaMuAyBtxufRsYhrY+bM1HZtOAsLyPrNbWjbt1H6u3sJdO3Gpk2xj4nENAuJinlE\nk1dNA7fbvq2qUlKcA10uIdj8bFx5M8Fv+U+HDg2gaWbK+50zH/09abNnEOhwIaX/+yDBIHzzjYNz\nzw0xc6bENAuJS/VNXk2xnG2FquIbeSnqwYM4FxUCkJ0NffsGWbFCY/due37TngmR6n2Odd8BYDqd\nOJctYfVqlcOHFQYODNCtm8Q0C4mL6fGglJZAKPbLLiNDfM62Ixa1cbRrIxWtZ39OLqX33B89Lp70\nBv6cXObPt16LAQMkCFxIbGI1natuCkq0hs3w98khlJ2N67NPcBbkA1a8M6Su39k9+e8AVAweStr0\nTwHIz9dQFJOcHBFnIbGJxDofmSUobg274XTiGzYSbf8+PE89BkCLFiadOwcpLNQ4fDjO84sDalER\nAN5nXySgt6ekBJYu1ejcOUSjRhJjKCQ2sSzBysWPTPx+e3bgTllxdhYW4Fi9yrq9ZnW0Q8rIkQH8\nfoW5c1PMevb50DZuINDmfEKt2+AbM5bFizV8PoX+/QPxnp0gnJDqmrzaueB+yoqzPyfXqvEcxvvC\nn/Hn5KZsSJ1z6WLUEi++QUOiY+JvFuzEsdwaYM9NwZQVZwDXnDxCjRtjOhykffYxAB07hmjRIsTs\n2Q7274/zBOsQ11dzAPAPHhodmz9fIy3NpGdPEWch8YnUdFaSpGxoSotzoH0HKoaPQgkECIX9VSUl\n4PUqlJUpDB7sSZnWVa65X2KmpeHr0w+AvXsV1q7V6NkzGM20EoREpjq3hp3Lhqa0OPvGjCVwSXfr\noF49AAxD5eBB61t21y41JVKV1Z9241i3Fn+fnOinecECq0KfuDQEu5BsraqSX3lOgD8szo4VywDQ\n9RCtW1tB7B6PWSVV2VlYgLOw4Kjn8Hph+XLVtlZ2xKXhO8KlAchmoGAboh24q2nyakfLuc53vXRd\nXwFEAtW2AM8A7wImsBb4rWEYdVa8Idi+A2aGB2dYnDMzYe7cEi65xENGBlUy4jJefA6AQzm50bG9\ne6FLl0x8PoV27YK2TG92RsR5kCXOpgn5+Q6ys006d5Y6GoI9EMv5DNB1PR1QDMMYGP53E/Bn4DHD\nMHIBBbi8LueEpuHv0hXN+B6l2PrOyMyE7t1D/PijSlGREk1tdi1cgGvhgmjYHcB//+vE57PeeFt2\n8A4EcOXPI9jyPIJt2wGwZYvCjh0q/foF0KT/gGATonHOEkp3WlwMZOi6nqfr+le6rvcGugH54ftn\nAkOO+ehaInBJdxTTxLFqZWyiF1u+1m+/VfHn5OJ97qXofSUPPoo/bD3v2RP7Rm7VKmS7im2O5ctQ\nDx3E94shoFhriYTQ9e8v/mbBPsRC6SqLs/XXjpZzXbs1SoGXgDeBdlhirBiGEUk/Kwbqn+hJGjTI\nwOE4PZOuSZOsowd/kQuvvUy2sQbGWeVEBwyAiRNh06YMrr4aeOLd2P//zuswZgQA69fHnuaRR1Ra\nt67m+euYatd4LBbPB8A9bgzu8OMWL7buGjcunSZN0mt6ejXCKa3RpsgaT5GWZwHgDvqin+Xmza27\nFCV+n+XTXWNdi/MGYFNYjDfour4Py3KOkAUcPNGTHDhwer9RmjTJoqio+Khxte2FNAIq5hdy+Fbr\n/latFCCTwkI/RUXlZP28l8hb6/vxJw4VFRMKQWFhJunpUF6u8PXXPq64ouK05lZTHGuNxyL78y9w\nOJ3s69wds6iYYBDmzs2kZUuTrKwSwhndCcWprtGOyBpPHaUcGgMVew9wOPy8gYAGZLBnTwVFRWeW\nw+31WtFcun7y1RlPtMbjCXdduzVuBiYC6Lp+NlAPyNN1fWD4/pHA0eEQtUyo+dkEm59tRWyE+1Q1\na2bSrFmI1astC13bsR1T0wg1boxj0wYIBtm0yQq7GzUqQHa2SWGhvbIKlaIinKtX4u/VJ7rTvWaN\ntab+/QMRL4cg2ILYhmDV2hpw5m4NrxcGDfIwcqSHgQPrJv+hrsX5LSBb1/UFwH+wxHo88LSu64sA\nFzC1jucEWH5nbc/PqLt2Rse6dAmye7fKz+v241i+FH/P3lQMH4W6fz+OVStYssQS7t69g/TuHWDb\nNpWdO+2jaK6v5wKxKA2AOXOsLxjJChRsR3o6pqZVG61xqhuCR4bNGobK1q2WXG7frnL55W4+/9xB\noBYjTevU1DMMwwdcW81dA+pyHtXhv6Q7aV9Mx7l8KRUtzgXg4otDzJoF6/71HZ1ME9+wkQRbnod7\nyvu4vprDkh3WpmCPHkEqKmDWLCeFhRpXXWWP2GDX3C8BovU0vF7461+tRq4vv5zGZZcFbBcWKKQw\n4SavNdGB2zPhcUxXGoc+nw1AdraJFe2r4HabrFnj4JZbHJx9dohrrvHTo0eQnj2DNXq92Czuq/YI\ndAsnoyxfFh3r0iUcsTHPCrHzDRuBv/8ATE3D9dWXLF2qkZVl0r59iL59rXMXLrSHa8NZkI/ry1kE\nm59NsENHAFauVCkrsz7EmzenRnakkFyYHs8R6dun1oHbWVhAgwG9ca5cgWvxIhpd2Bb365OYPs0B\nKNwzbhPffedlwYISbrnFx8GDChMnpnH11RkMH55Ro+4OufrC+C/qgqmq0WQUgIsussLiVm7OJtC6\nDcG27TDrZxPo3pMDy7fxww8q3boF0TS48MJQ2O9sj8Bgz1OPoRYXW1Zz2Lm8e7c0chXsjZmZiVJ6\ndIbgyRbc9/fuCxXl0WO1aA8Zjz/Chy/uIUMp5bENN1GvaDPtnZt44fb1fPCnH6Ln1nSegz3MvLog\nM5Ng+444vl1lNX11OmnSxKRF41KW7+1CxdARURHzDR7KN4sbAzHfrKpC794BZs1ysmOHwrnnJmZx\nemdhARkvPodzzWrreNkSnIUF+HNyyc+3Pg6vvlomLg3BlpgeD8rOHdFjhwPS0k6+A3faRx/i2LwZ\nf6fO+IaPQv1xF/PWN2fLqpbcxNs0WrsAenWJnj8UD+1Zyvd0QHdvpdMBA+hbI2sRy7kS/m49UMrL\ncaz/LjrWLdPgZ5qxrfvY6Jhv0BAKyQGqbpz16xdxbSSu9ezPycX7/MTocfGrf8efkxsOodNo1izE\nVVeJMAv2xPRkopSVUXmn7qQ7cJeX4/nTs5gOB4f/+R9KH3wU3+ChTG71DAC38qZ12qWjKbv2esqu\nvR7HqEEspQff0Iu8z/aRNqRmhBlEnKtwlN/ZNOl+wKo7sUzrGTuv00UUOgaiEuSSLv7oeMTvnOgh\nde63JwMQaHsBrjl5gNWOav9+lWHDJIROsC/VNXk92Q7c7nfeRNu5g7Lb7yR0TgsAdueMY8YMB+0b\n/cxF9w2g5P6HCHbshPflSXhfnkSw44Uo999Np/sH0WjOxzW6FhHnSkQq1EX8ztoGg56HrIiG1d+l\nRc+r8KssC3XlYlaTvfXb6HjHjpbfOZEtZwBl314ASh94iIDeHoC8PGvOw4fbI9JEEKqjum4oJ2M5\nK4cPkfHyi4Tq1ad0/P9Gxz/6yIHPp3D94O2UPfgIpb9/JHrNgFUTvvT3R4/XBCLOlQi2u4BQZla0\nfKhr9ky6sRyAVatigvvttyoVIRd9WRgttwmW37lPnwDbt6ts356g5qdp4jDWY6anUzF0BL4xlrsm\nL8+B221GXTOCYEdiTV5PzXJ2v/YK6oEDlP7uXswGDa3nMmHKFCcul8m4pztEz41cM8e7XROIOFdG\n0wh0vQTHxg0ohw6S9uUsGqoHOa+Fn9Wr1UjyIEuXWkLdl4XRcpsRcnIS2++sfb8exwYD35Dh0Xqo\nW7YobNigMWBAQLqeCLbGzIh0Q4mlTHs8JuXlyjETRtSfdpPx+iSCzZpTduuvo+NLl6oYhsaoUYG4\ndJ8XcT6CSGcU11dzcCxdTKB7Ty6+BPbti2X/RTIDe3Yqxrl0McqhWDmQRI93Tpv2CQAVl8e+5fPy\nrLkOGyZWs2Bvjt/k9ejznYUFZN5/D0pZGaUPPBw7GZgyxUrIuu46/9EPrANEnI8g4nfOmPgCSihE\nxbARXHyxFe+7apWGaVqWc/PmIZqN6IwSDOKcnx99fMeOIRo0SNB4Z9MkbfqnmG43FUOGR4cj4jx0\nqPibBXsTcWs4li6OjkVSuH35S4463zPhCVx5Mwm0bUf5Nb+MjhcXw7RpDlq2DJGbGx+jRcT5CKJt\nqzYYAPiGjYxmCq5erbJ1q0JRkUqPHkH8g620Z9e8o/3OO3Yknt9ZW/cdjk0brZjt8K724cOwaJFG\n165BzjorMWOzBeFkiURrpH/0n+hYJEsw+NpbgOXySH/zDRr07opz5XIUAM2Bc/Gi6GM++cRJaanC\nddf5UeOkkon52zuOmGedhelKQ/FVWN1B9PZc1NwS51WrNNq1s6zonj2DBLpcQqhhQ1wz/otz3JX4\n+/UHLL/zjBlOFi7UaNkycazRtOlHuzS++spBIKAwbFjizFMQTgdnYQHuyf8AwLHRoGGndgRbtKTR\n+luB2/GvXE/jlk1RysuPeuzhye8SbB/b9Hv/fSeKYjJmTHxcGiCWcxUi7agUX7gms8+Hc+EC6teH\nNm1CfPutFvU39+gRBE3DN3AQ2v59eCY8Hn2ehIx3Nk3Spn2KmZGBb/Cw6PDs2RF/s4izYG/8ObmU\n3P9g9Fjb8zOuFUvJLLOKknvJxHQ68fXrT+kdv6Vi5KWU3XgzJfc9SNrnn0UfN3WqgzVrNExT4YYb\n3HFr3JxA6hF//Dm5eBs1pmH/XgB4H58QbUfVpUuQTz5x8sUXVshZp04hnIUFOL614pydq1ZS/4pR\nlD7wMB365NKgQWLFO2tr1+DY/APlV4yLbnoEAjB3roNzzgnRqZPU0RDsj2PTRkp/czeKrwJTUSi/\n9Q7S7toKy2DfqKspuzDX2vgDXNM/jYa/uaZ/Cljx/nffHeuYEqmX0a1b3V8fYjkfQdr0Tym5/yFK\nf30Xjq2bo+ORnoL796t07RrE6bTEvHjiK9FzvBOew5+Ti6pCjx6W3/n77xPD75we/vBVjBkXHVu6\nVOPgQYWhQyUrUEgOAu07UPL0M3ifewl/774E27Qlvd05AOz/PzdXSRQ5Mkb5q680br7ZjdMJLVpY\nYhzPAmAizkcQyfgpmfBslTeyS5fYG1S5noarIB9/OO0786lHAasu8sqVltU8dmzNlhE8LUyTtGmf\nYGZ48A2OFdaPuDQkK1BIFqpLCknr1RmwKtMdK1EkP1/jxhvdqCp88EEZ8+eXMHNmCbNnl8atzoyI\n8xEcK+Onc+cgVrHtyG2LQPsOHPrPp4SaNMW55BvUHdsxDJWiIuul3bdPreLeOLLDQgSvF5YvV2tF\nyB3frkLbuoWKESOpnGWSl6eRkWFGE2cEIRk5UcH9wkKNG25wY5rw7rtl9O9vFc3v1u3kewXWBiLO\np4DTaf195pm0qIj6xozFrFcf75N/QPH5yHziEXQ9RLt2McGbOtUZvZ3x/B/x/PHJKs+7axd06JDJ\nyJEehg2reUvbPelVoKpLY+1ahU2bNHJyAqQnZoNtQagRjldwf948jauvduP3wzvvlDFoUOIYKiLO\nJ4lhqPj9kS4hRxfVrrjyavy9+pD2xXQaLJ3L7NmlfPFFCRdeGOSzz5yseGsN2SMH41q8COfyZTTI\n6Y6zsIBQCO64w01FhfXcmzaduGD3sazvijkLWfy35VXF3e/HP2Me3yi92X3xEObP13jiCRcjRljm\nxOrVWvzdLoJQi8Qs56rje/fCtdda116TJiZ9+iSOMINEa5w0EWt440at+k0CRaH4uZdoMCSXzEce\nwP/1Inr0SOP55ysYPTqDB9+9mCX7KhUB37gB7ft1vLZ8MEuWWBEgkRZRJ9odzvjTsygVFRx+/W0A\n9h/UmD63Hk/9qR/ekAePy8fQpitpdGgL7uI9/BuDfTRG6RrCPOL7eM8eNW670YJQFxzLcn7zaeI4\n6QAACU5JREFUTSfBYKwLUKJdB2I5nySZmTB7dulxNwmCnTpTftOtOH7YhPv1SQD06hXkysE/s9rw\n8P7eS/H1H0jZjTcTyvCw/OH/8uwzTpo3DzF/fgmvv16Gx2Py0EPprF5tvTWVreS0D6fQsEsHfItW\nMWNFc97u8R7/02MvHYZewP3Pt8AbskyEEp+Lz3b24q3iq3mN37EPq2uLicq4cX7eeaeU88+3rARp\nRyUkO9VZzqYJeXlOIvtIiXgdiOV8CkQ2CY5HyUOPkTbtEzwvPkfwvFaYTZoycdE9zGA5j6T/mYFv\nKdSvDzubdePqF69EDQX5Z49XaLu9PW2bqmS+MZBf/tLNDTe4ycsrRX92AsreIsz69XGuWskC+jKC\n7ykh9u3Qs9FGRjT8hg829mUz59Ou0T6m/HUXgRbncei1/3DbzCvZWdyACxru4aWX3GRmwoABpRiG\niq7Hd9NDEGqbiOVceUNwxQqVtWs1hgzxc999voS8DkScaxizfjbexydQb/ydZN17F0ogQP1gkPvH\nbeDpTy7hpZd8PPlkBTfOv52fQw5ebPI8g6c/TGhRU4LntWLUAz6eGpTFk3MHc/vFa5kXWkkaPtbS\nkcez5/LZwUFV/r8PPihl2LBmZPxpHXf6NrG1pAWtMnehDrkPANewdOY/78AwSuj8wxxcmaOBk/ui\nEYRkIFL4qHJVurfftirO3XGHP2GvAxHnGsZZWED6h1MAUL1eTFWl5LGnufW2dry3IsSbbzoxDJVF\nixxcdpmfW/+nFaG7MlGL9qAW7SH7qrE8Dhh8wL9C13EdH1BCJrMYAQcVurYqYo+/Ebt2qVzQ7CB9\n+1pheoH2HVDHjKVXkywOvfU+vvB8fGPGkklYiLuNjstrIgjxJNaB27Kc9+5VmDbNQdu2Qfr3T6xN\nwMqIz7mG8efk4n3hz9Hjw5PeoOyu8aSlwaOPlhMMKnz9tQOn0+TZZ8vxj7qUQ1OnR88vvfEmDr/1\nT17I78xFTXbxMVcyi5GkaUEmTy5l1uJ0CgqsAPlZC7XoT7Ha7MggCHbG5QKnM9aBe8oUJz6fwk03\n+RM6M1Ys51ogkgIO4Nj8Q9SKPeecWElOv19h1y6VZs1CuObkRc9HUfCNvpw04OGrl3DNX63U04qg\ngxYtKlAUcUkIwqlitaqCYBDee89JRobJVVfFr+LcySDiXAsE2nc4qqAKQPv2Idq2DbJpU9VwvGOd\n3+venrSbdZzwPUEQTgqryatCXp6DnTtVbrzRR7168Z7V8VFM034F1ouKik9r0k2aZFFUVHziE2sR\nr5dTipI41fMTYY21jawxOajLNfbtm8HBgwoXXhgiP99Bfn4JHTrUvrFzojU2aZJ1TMeKWM51zKm6\nJMSFIQhnjscDmzcr5Oc76Ns3UCfCfKbIhqAgCEmPx2MSCllG6s03J7avOYKIsyAISY/LCmumadMQ\nI0fao0SuiLMgCEmN1wvLloXzAQJQURHnCZ0kIs6CICQ1hqHi9Voujf371RNWfUwU7DFLQRCE06Ry\nfXU7haRKtIYgCElNpKKk3Qp9iTgLgpD02DEkVdwagiAICYiIsyAIQgIi4iwIgpCAiDgLgiAkICLO\ngiAICYiIsyAIQgIi4iwIgpCAiDgLgiAkICLOgiAICYiIsyAIQgJiyzZVgiAIyY5YzoIgCAmIiLMg\nCEICIuIsCIKQgIg4C4IgJCAizoIgCAmIiLMgCEICkhKdUHRdV4G/ARcDFcCthmFsiu+sagZd13sB\nLxiGMVDX9bbAu4AJrAV+axiGvdo/HIGu607gbaAVkAb8EVhHEq1T13UNmAzoWGv6NVBOEq0RQNf1\npsByYCgQIMnWB6Dr+grgcPhwC/AMp7nOVLGcrwDSDcPoAzwETIzzfGoEXdd/D7wJpIeH/gw8ZhhG\nLqAAl8drbjXIL4F94TWNAF4j+dY5GsAwjBzgMawLOqnWGP6SfR0oCw8l1foAdF1PBxTDMAaG/93E\nGawzVcS5HzALwDCMb4Du8Z1OjfEDMK7ScTcgP3x7JjCkzmdU83wEPB6+rWBZXEm1TsMwPgNuDx+e\nBxwkydYIvAT8A/gxfJxs6wPrl3mGrut5uq5/pet6b85gnakizvWAQ5WOg7qu296lYxjGx4C/0pBi\nGEYk5bMYqF/3s6pZDMPwGoZRrOt6FjAVy7JMxnUGdF1/D/grMIUkWqOu678CigzDmF1pOGnWV4lS\nrC+h4ViuqTN6H1NFnA8DWZWOVcMwAvGaTC1S2ZeVhWWB2R5d188F5gH/NAzjXyTpOg3DuBG4AMv/\n7K50l93XeDMwVNf1r4EuwPtA00r32319ETYAHxiGYRqGsQHYB5xV6f5TWmeqiHMhMAog/FNjTXyn\nU2us1HV9YPj2SKAgjnOpEXRdPwvIAx40DOPt8HBSrVPX9et1XX84fFiK9eWzLFnWaBhGf8MwBhiG\nMRBYBdwAzEyW9VXiZsL7Wbqun431iz3vdNdp+5/2J8mnWN/cC7H8ljfFeT61xX3AZF3XXcB6LDeA\n3XkEaAA8rut6xPc8Hng1idb5CfCOruvzASdwD9a6ku29rEwyflbfAt7VdX0BVnTGzcBeTnOdUpVO\nEAQhAUkVt4YgCIKtEHEWBEFIQEScBUEQEhARZ0EQhARExFkQBCEBEXEWUgJd108pLEnX9ad0XX+q\nlqYjCCdExFkQBCEBSZUkFEEAIJyt9QhWJl4HrGzRaw3D8Om6/gBWAaK9wAFgSfgxI4AJWAkiW4Db\ngAys8pcDsApQLQMeNgzji7pcj5C8iOUspCJ9gbuwxLklMFzX9e5YGV1dsSqHtQDQdb0J8Dww3DCM\nrsBsrPrZO4AHgb8DTwILRZiFmkQsZyEVWWsYxk4AXdfXAw2xCt3PMAzDGx7/CNCAXlgCPk/XdcJj\n+wEMw3hH1/X/C1wLdKrrRQjJjYizkIqUV7ptYtVbMan6SzKAJcQasMAwjDEQLaieVen2uVjXUQvA\nqPWZCymDuDUEwWIucJmu6/XDojs2PL4Y6KPr+gXh48eBF8O3/wB8BdyLVbhIriehxpAPkyAAhmGs\nAl4GlmJ1rtgWHv8Jyxf9/3RdXwNcAtyn63of4ErgUcMwpmK5Ou6Px9yF5ESq0gmCICQgYjkLgiAk\nICLOgiAICYiIsyAIQgIi4iwIgpCAiDgLgiAkICLOgiAICYiIsyAIQgIi4iwIgpCA/H++6dYmY1Ov\nlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1bacaceb828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's plot the first 50 actual and predicted values of pm2.5.\n",
    "plt.figure(figsize=(5.5, 5.5))\n",
    "plt.plot(range(50), df_val['pm2.5'].loc[7:56], linestyle='-', marker='*', color='r')\n",
    "plt.plot(range(50), pred_pm25[:50], linestyle='-', marker='.', color='b')\n",
    "plt.legend(['Actual','Predicted'], loc=2)\n",
    "plt.title('Actual vs Predicted pm2.5')\n",
    "plt.ylabel('pm2.5')\n",
    "plt.xlabel('Index')\n",
    "plt.savefig('plots/ch5/B07887_05_09.png', format='png', dpi=300)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
